exp_final_test – Complete Experiment Report
Base_Gaussian
(MvNormal,
mu,
12 runs)
Pooled Chains results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
(0, 0) |
-2.078 |
0.0498 |
-0.905 |
| SMC |
(0, 0) |
-1.772 |
0.0903 |
-0.719 |
| Metro |
(0, 0) |
1.885 |
0.0818 |
1.829 |
| DEMetro_Z |
(0, 0) |
5.101 |
6.41e-05 |
2.695 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
-8.309
|
4.55e-06
|
-2.399
|
| Metro_vs_SMC |
0
|
2.475
|
0.0309
|
0.714
|
| Metro_vs_DEMetro_Z |
0
|
-0.865
|
0.406
|
-0.250
|
| HMC_vs_Metro |
0
|
-2.719
|
0.02
|
-0.785
|
| HMC_vs_SMC |
0
|
-0.530
|
0.607
|
-0.153
|
| DEMetro_Z_vs_SMC |
0
|
6.548
|
4.15e-05
|
1.890
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
(0, 0) |
0.018 |
0.025 |
0.008 |
-0.905 |
| SMC |
(0, 0) |
0.019 |
0.025 |
0.008 |
-0.719 |
| Metro |
(0, 0) |
0.040 |
0.025 |
0.008 |
1.829 |
| DEMetro_Z |
(0, 0) |
0.047 |
0.025 |
0.008 |
2.695 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
(0, 0) |
1.121 |
0.274 |
0.430 |
| SMC |
(0, 0) |
-0.037 |
0.971 |
-0.018 |
| Metro |
(0, 0) |
1.245 |
0.227 |
0.595 |
| DEMetro_Z |
(0, 0) |
0.578 |
0.57 |
0.277 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
0.929
|
0.373
|
0.268
|
| Metro_vs_DEMetro_Z |
0
|
0.641
|
0.535
|
0.185
|
| HMC_vs_Metro |
0
|
-0.571
|
0.579
|
-0.165
|
| HMC_vs_DEMetro_Z |
0
|
0.326
|
0.751
|
0.094
|
| Metro_vs_SMC |
0
|
1.553
|
0.149
|
0.448
|
| DEMetro_Z_vs_SMC |
0
|
0.614
|
0.552
|
0.177
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
(0, 0) |
0.036 |
0.030 |
0.013 |
0.430 |
| SMC |
(0, 0) |
0.030 |
0.030 |
0.013 |
-0.018 |
| Metro |
(0, 0) |
0.038 |
0.030 |
0.013 |
0.595 |
| DEMetro_Z |
(0, 0) |
0.034 |
0.030 |
0.013 |
0.277 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
(0, 0) |
-1.658 |
0.114 |
-0.865 |
| SMC |
(0, 0) |
-2.133 |
0.045 |
-1.006 |
| Metro |
(0, 0) |
2.367 |
0.0358 |
3.448 |
| DEMetro_Z |
(0, 0) |
6.598 |
1.32e-05 |
5.703 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
-1.467
|
0.171
|
-0.423
|
| DEMetro_Z_vs_SMC |
0
|
7.708
|
9.28e-06
|
2.225
|
| HMC_vs_DEMetro_Z |
0
|
-7.200
|
1.75e-05
|
-2.079
|
| HMC_vs_Metro |
0
|
-2.879
|
0.015
|
-0.831
|
| HMC_vs_SMC |
0
|
0.351
|
0.733
|
0.101
|
| Metro_vs_SMC |
0
|
2.899
|
0.0145
|
0.837
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
(0, 0) |
0.029 |
0.032 |
0.004 |
-0.865 |
| SMC |
(0, 0) |
0.028 |
0.032 |
0.004 |
-1.006 |
| Metro |
(0, 0) |
0.046 |
0.032 |
0.004 |
3.448 |
| DEMetro_Z |
(0, 0) |
0.056 |
0.032 |
0.004 |
5.703 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
(0, 0) |
-2.071 |
0.0504 |
-0.808 |
| SMC |
(0, 0) |
-1.961 |
0.0629 |
-0.755 |
| Metro |
(0, 0) |
1.673 |
0.119 |
1.919 |
| DEMetro_Z |
(0, 0) |
4.303 |
0.000631 |
3.131 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
5.293
|
0.000255
|
1.528
|
| HMC_vs_Metro |
0
|
-2.407
|
0.0348
|
-0.695
|
| Metro_vs_DEMetro_Z |
0
|
-0.985
|
0.346
|
-0.284
|
| HMC_vs_SMC |
0
|
-0.190
|
0.853
|
-0.055
|
| Metro_vs_SMC |
0
|
2.304
|
0.0417
|
0.665
|
| HMC_vs_DEMetro_Z |
0
|
-5.401
|
0.000216
|
-1.559
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
(0, 0) |
0.013 |
0.016 |
0.004 |
-0.808 |
| SMC |
(0, 0) |
0.013 |
0.016 |
0.004 |
-0.755 |
| Metro |
(0, 0) |
0.023 |
0.016 |
0.004 |
1.919 |
| DEMetro_Z |
(0, 0) |
0.027 |
0.016 |
0.004 |
3.131 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
R Hat (scatter)
Mode Transitions
One Chain results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
(0, 0) |
-2.509 |
0.0201 |
-0.964 |
| SMC |
(0, 0) |
-2.399 |
0.0254 |
-1.015 |
| Metro |
(0, 0) |
0.841 |
0.412 |
0.502 |
| DEMetro_Z |
(0, 0) |
2.239 |
0.039 |
1.367 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
-3.563
|
0.00445
|
-1.029
|
| Metro_vs_SMC |
0
|
2.438
|
0.0329
|
0.704
|
| Metro_vs_DEMetro_Z |
0
|
-0.996
|
0.341
|
-0.288
|
| HMC_vs_Metro |
0
|
-2.923
|
0.0139
|
-0.844
|
| HMC_vs_SMC |
0
|
0.159
|
0.877
|
0.046
|
| DEMetro_Z_vs_SMC |
0
|
4.088
|
0.0018
|
1.180
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
(0, 0) |
0.017 |
0.025 |
0.008 |
-0.964 |
| SMC |
(0, 0) |
0.017 |
0.025 |
0.008 |
-1.015 |
| Metro |
(0, 0) |
0.029 |
0.025 |
0.008 |
0.502 |
| DEMetro_Z |
(0, 0) |
0.036 |
0.025 |
0.008 |
1.367 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
(0, 0) |
2.035 |
0.0565 |
1.110 |
| SMC |
(0, 0) |
-0.800 |
0.433 |
-0.367 |
| Metro |
(0, 0) |
1.684 |
0.11 |
0.960 |
| DEMetro_Z |
(0, 0) |
2.108 |
0.0488 |
1.140 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
3.331
|
0.0067
|
0.961
|
| Metro_vs_DEMetro_Z |
0
|
-0.305
|
0.766
|
-0.088
|
| HMC_vs_Metro |
0
|
0.181
|
0.86
|
0.052
|
| HMC_vs_DEMetro_Z |
0
|
-0.052
|
0.959
|
-0.015
|
| Metro_vs_SMC |
0
|
1.894
|
0.0849
|
0.547
|
| DEMetro_Z_vs_SMC |
0
|
2.384
|
0.0363
|
0.688
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
(0, 0) |
0.045 |
0.030 |
0.013 |
1.110 |
| SMC |
(0, 0) |
0.025 |
0.030 |
0.013 |
-0.367 |
| Metro |
(0, 0) |
0.043 |
0.030 |
0.013 |
0.960 |
| DEMetro_Z |
(0, 0) |
0.045 |
0.030 |
0.013 |
1.140 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
(0, 0) |
-0.633 |
0.534 |
-0.316 |
| SMC |
(0, 0) |
-2.821 |
0.0102 |
-1.271 |
| Metro |
(0, 0) |
2.280 |
0.038 |
1.727 |
| DEMetro_Z |
(0, 0) |
5.099 |
0.000175 |
4.460 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
-2.523
|
0.0283
|
-0.728
|
| DEMetro_Z_vs_SMC |
0
|
6.709
|
3.34e-05
|
1.937
|
| HMC_vs_DEMetro_Z |
0
|
-4.888
|
0.000481
|
-1.411
|
| HMC_vs_Metro |
0
|
-2.576
|
0.0258
|
-0.744
|
| HMC_vs_SMC |
0
|
2.214
|
0.0489
|
0.639
|
| Metro_vs_SMC |
0
|
3.533
|
0.00469
|
1.020
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
(0, 0) |
0.031 |
0.032 |
0.004 |
-0.316 |
| SMC |
(0, 0) |
0.027 |
0.032 |
0.004 |
-1.271 |
| Metro |
(0, 0) |
0.039 |
0.032 |
0.004 |
1.727 |
| DEMetro_Z |
(0, 0) |
0.051 |
0.032 |
0.004 |
4.460 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
(0, 0) |
-0.783 |
0.442 |
-0.333 |
| SMC |
(0, 0) |
-2.261 |
0.0341 |
-0.980 |
| Metro |
(0, 0) |
1.028 |
0.317 |
0.568 |
| DEMetro_Z |
(0, 0) |
3.799 |
0.00156 |
2.472 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
5.778
|
0.000123
|
1.668
|
| HMC_vs_Metro |
0
|
-1.463
|
0.171
|
-0.422
|
| Metro_vs_DEMetro_Z |
0
|
-2.909
|
0.0142
|
-0.840
|
| HMC_vs_SMC |
0
|
1.596
|
0.139
|
0.461
|
| Metro_vs_SMC |
0
|
2.432
|
0.0333
|
0.702
|
| HMC_vs_DEMetro_Z |
0
|
-4.215
|
0.00145
|
-1.217
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
(0, 0) |
0.015 |
0.016 |
0.004 |
-0.333 |
| SMC |
(0, 0) |
0.013 |
0.016 |
0.004 |
-0.980 |
| Metro |
(0, 0) |
0.018 |
0.016 |
0.004 |
0.568 |
| DEMetro_Z |
(0, 0) |
0.025 |
0.016 |
0.004 |
2.472 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
Mode Transitions
KDE + Init Plots
Forest & Ridge Plots
Pooled
Chain
Pairwise Scatter Plots
Pooled
Chain
Base_Gaussian_Seed
(MvNormal,
mu,
12 runs)
Pooled Chains results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
(0, 0) |
-0.544 |
0.593 |
-0.183 |
| SMC |
(0, 0) |
-0.182 |
0.857 |
-0.068 |
| Metro |
(0, 0) |
3.252 |
0.00424 |
1.734 |
| DEMetro_Z |
(0, 0) |
2.609 |
0.0191 |
1.728 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
-3.644
|
0.00386
|
-1.052
|
| Metro_vs_SMC |
0
|
3.518
|
0.00481
|
1.016
|
| Metro_vs_DEMetro_Z |
0
|
0.009
|
0.993
|
0.003
|
| HMC_vs_Metro |
0
|
-4.839
|
0.00052
|
-1.397
|
| HMC_vs_SMC |
0
|
-0.317
|
0.757
|
-0.092
|
| DEMetro_Z_vs_SMC |
0
|
2.351
|
0.0384
|
0.679
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
(0, 0) |
0.016 |
0.018 |
0.011 |
-0.183 |
| SMC |
(0, 0) |
0.018 |
0.018 |
0.011 |
-0.068 |
| Metro |
(0, 0) |
0.037 |
0.018 |
0.011 |
1.734 |
| DEMetro_Z |
(0, 0) |
0.037 |
0.018 |
0.011 |
1.728 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
(0, 0) |
-0.133 |
0.896 |
-0.064 |
| SMC |
(0, 0) |
-1.255 |
0.223 |
-0.481 |
| Metro |
(0, 0) |
0.296 |
0.771 |
0.189 |
| DEMetro_Z |
(0, 0) |
2.084 |
0.0549 |
1.542 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
1.171
|
0.266
|
0.338
|
| Metro_vs_DEMetro_Z |
0
|
-1.796
|
0.1
|
-0.518
|
| HMC_vs_Metro |
0
|
-0.449
|
0.662
|
-0.130
|
| HMC_vs_DEMetro_Z |
0
|
-3.240
|
0.00787
|
-0.935
|
| Metro_vs_SMC |
0
|
1.458
|
0.173
|
0.421
|
| DEMetro_Z_vs_SMC |
0
|
3.079
|
0.0105
|
0.889
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
(0, 0) |
0.031 |
0.032 |
0.011 |
-0.064 |
| SMC |
(0, 0) |
0.027 |
0.032 |
0.011 |
-0.481 |
| Metro |
(0, 0) |
0.034 |
0.032 |
0.011 |
0.189 |
| DEMetro_Z |
(0, 0) |
0.049 |
0.032 |
0.011 |
1.542 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
(0, 0) |
-1.080 |
0.295 |
-0.352 |
| SMC |
(0, 0) |
-0.777 |
0.446 |
-0.322 |
| Metro |
(0, 0) |
3.770 |
0.00163 |
2.410 |
| DEMetro_Z |
(0, 0) |
4.511 |
0.000459 |
3.536 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
-1.216
|
0.25
|
-0.351
|
| DEMetro_Z_vs_SMC |
0
|
4.321
|
0.00121
|
1.247
|
| HMC_vs_DEMetro_Z |
0
|
-5.577
|
0.000166
|
-1.610
|
| HMC_vs_Metro |
0
|
-5.662
|
0.000146
|
-1.635
|
| HMC_vs_SMC |
0
|
-0.081
|
0.937
|
-0.023
|
| Metro_vs_SMC |
0
|
4.712
|
0.000637
|
1.360
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
(0, 0) |
0.027 |
0.029 |
0.007 |
-0.352 |
| SMC |
(0, 0) |
0.027 |
0.029 |
0.007 |
-0.322 |
| Metro |
(0, 0) |
0.045 |
0.029 |
0.007 |
2.410 |
| DEMetro_Z |
(0, 0) |
0.052 |
0.029 |
0.007 |
3.536 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
(0, 0) |
-0.474 |
0.641 |
-0.163 |
| SMC |
(0, 0) |
-1.037 |
0.311 |
-0.441 |
| Metro |
(0, 0) |
3.159 |
0.00631 |
2.189 |
| DEMetro_Z |
(0, 0) |
4.427 |
0.000422 |
2.903 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
4.507
|
0.000891
|
1.301
|
| HMC_vs_Metro |
0
|
-4.149
|
0.00162
|
-1.198
|
| Metro_vs_DEMetro_Z |
0
|
-0.874
|
0.401
|
-0.252
|
| HMC_vs_SMC |
0
|
0.690
|
0.505
|
0.199
|
| Metro_vs_SMC |
0
|
4.580
|
0.00079
|
1.322
|
| HMC_vs_DEMetro_Z |
0
|
-5.572
|
0.000167
|
-1.608
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
(0, 0) |
0.013 |
0.014 |
0.004 |
-0.163 |
| SMC |
(0, 0) |
0.012 |
0.014 |
0.004 |
-0.441 |
| Metro |
(0, 0) |
0.022 |
0.014 |
0.004 |
2.189 |
| DEMetro_Z |
(0, 0) |
0.025 |
0.014 |
0.004 |
2.903 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
R Hat (scatter)
Mode Transitions
One Chain results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
(0, 0) |
0.270 |
0.789 |
0.107 |
| SMC |
(0, 0) |
-0.398 |
0.695 |
-0.159 |
| Metro |
(0, 0) |
1.278 |
0.215 |
0.545 |
| DEMetro_Z |
(0, 0) |
2.412 |
0.026 |
1.248 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
-2.569
|
0.0261
|
-0.742
|
| Metro_vs_SMC |
0
|
1.396
|
0.19
|
0.403
|
| Metro_vs_DEMetro_Z |
0
|
-1.196
|
0.257
|
-0.345
|
| HMC_vs_Metro |
0
|
-0.876
|
0.4
|
-0.253
|
| HMC_vs_SMC |
0
|
0.720
|
0.487
|
0.208
|
| DEMetro_Z_vs_SMC |
0
|
3.540
|
0.00463
|
1.022
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
(0, 0) |
0.020 |
0.018 |
0.011 |
0.107 |
| SMC |
(0, 0) |
0.017 |
0.018 |
0.011 |
-0.159 |
| Metro |
(0, 0) |
0.024 |
0.018 |
0.011 |
0.545 |
| DEMetro_Z |
(0, 0) |
0.032 |
0.018 |
0.011 |
1.248 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
(0, 0) |
0.190 |
0.851 |
0.104 |
| SMC |
(0, 0) |
-3.001 |
0.00661 |
-1.283 |
| Metro |
(0, 0) |
0.544 |
0.594 |
0.384 |
| DEMetro_Z |
(0, 0) |
4.001 |
0.00117 |
2.937 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
2.298
|
0.0422
|
0.663
|
| Metro_vs_DEMetro_Z |
0
|
-2.744
|
0.0191
|
-0.792
|
| HMC_vs_Metro |
0
|
-0.309
|
0.763
|
-0.089
|
| HMC_vs_DEMetro_Z |
0
|
-3.096
|
0.0102
|
-0.894
|
| Metro_vs_SMC |
0
|
2.151
|
0.0546
|
0.621
|
| DEMetro_Z_vs_SMC |
0
|
5.164
|
0.000311
|
1.491
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
(0, 0) |
0.033 |
0.032 |
0.011 |
0.104 |
| SMC |
(0, 0) |
0.018 |
0.032 |
0.011 |
-1.283 |
| Metro |
(0, 0) |
0.036 |
0.032 |
0.011 |
0.384 |
| DEMetro_Z |
(0, 0) |
0.064 |
0.032 |
0.011 |
2.937 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
(0, 0) |
0.837 |
0.412 |
0.319 |
| SMC |
(0, 0) |
-1.836 |
0.0817 |
-0.641 |
| Metro |
(0, 0) |
2.456 |
0.0225 |
1.068 |
| DEMetro_Z |
(0, 0) |
6.305 |
3.78e-06 |
3.123 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
-3.332
|
0.00669
|
-0.962
|
| DEMetro_Z_vs_SMC |
0
|
10.048
|
7.05e-07
|
2.900
|
| HMC_vs_DEMetro_Z |
0
|
-6.797
|
2.96e-05
|
-1.962
|
| HMC_vs_Metro |
0
|
-1.545
|
0.151
|
-0.446
|
| HMC_vs_SMC |
0
|
3.273
|
0.00742
|
0.945
|
| Metro_vs_SMC |
0
|
4.066
|
0.00187
|
1.174
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
(0, 0) |
0.031 |
0.029 |
0.007 |
0.319 |
| SMC |
(0, 0) |
0.025 |
0.029 |
0.007 |
-0.641 |
| Metro |
(0, 0) |
0.036 |
0.029 |
0.007 |
1.068 |
| DEMetro_Z |
(0, 0) |
0.050 |
0.029 |
0.007 |
3.123 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
(0, 0) |
1.199 |
0.243 |
0.501 |
| SMC |
(0, 0) |
-1.386 |
0.18 |
-0.588 |
| Metro |
(0, 0) |
1.717 |
0.101 |
0.832 |
| DEMetro_Z |
(0, 0) |
5.391 |
2.82e-05 |
2.664 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
7.372
|
1.41e-05
|
2.128
|
| HMC_vs_Metro |
0
|
-0.571
|
0.58
|
-0.165
|
| Metro_vs_DEMetro_Z |
0
|
-3.024
|
0.0116
|
-0.873
|
| HMC_vs_SMC |
0
|
2.673
|
0.0217
|
0.772
|
| Metro_vs_SMC |
0
|
2.682
|
0.0213
|
0.774
|
| HMC_vs_DEMetro_Z |
0
|
-4.089
|
0.00179
|
-1.180
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
(0, 0) |
0.016 |
0.014 |
0.004 |
0.501 |
| SMC |
(0, 0) |
0.011 |
0.014 |
0.004 |
-0.588 |
| Metro |
(0, 0) |
0.017 |
0.014 |
0.004 |
0.832 |
| DEMetro_Z |
(0, 0) |
0.024 |
0.014 |
0.004 |
2.664 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
Mode Transitions
KDE + Init Plots
Forest & Ridge Plots
Pooled
Chain
Pairwise Scatter Plots
Pooled
Chain
Vary_only_Correlation
(MvNormal,
correlation,
12 runs)
Pooled Chains results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
-2.644 |
0.0151 |
-0.984 |
| HMC |
0.3 |
-0.503 |
0.621 |
-0.250 |
| HMC |
0.5 |
1.219 |
0.237 |
0.608 |
| HMC |
0.9 |
0.570 |
0.575 |
0.250 |
| HMC |
0.95 |
0.750 |
0.462 |
0.376 |
| HMC |
0.99 |
1.363 |
0.191 |
0.854 |
| SMC |
0.0 |
-2.871 |
0.00903 |
-1.288 |
| SMC |
0.3 |
-0.415 |
0.683 |
-0.214 |
| SMC |
0.5 |
-0.929 |
0.363 |
-0.412 |
| SMC |
0.9 |
0.502 |
0.621 |
0.226 |
| SMC |
0.95 |
-0.426 |
0.675 |
-0.146 |
| SMC |
0.99 |
0.625 |
0.539 |
0.217 |
| Metro |
0.0 |
2.021 |
0.0567 |
0.976 |
| Metro |
0.3 |
2.856 |
0.00964 |
1.376 |
| Metro |
0.5 |
0.444 |
0.663 |
0.272 |
| Metro |
0.9 |
2.666 |
0.0205 |
3.582 |
| Metro |
0.95 |
6.056 |
6.66e-05 |
10.993 |
| Metro |
0.99 |
4.344 |
0.00113 |
14.022 |
| DEMetro_Z |
0.0 |
1.801 |
0.0952 |
1.853 |
| DEMetro_Z |
0.3 |
3.707 |
0.00276 |
4.057 |
| DEMetro_Z |
0.5 |
2.894 |
0.00987 |
1.685 |
| DEMetro_Z |
0.9 |
2.232 |
0.0421 |
1.762 |
| DEMetro_Z |
0.95 |
2.514 |
0.0232 |
1.696 |
| DEMetro_Z |
0.99 |
5.132 |
4.49e-05 |
2.394 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0.0
|
-2.733
|
0.0195
|
-0.789
|
| HMC_vs_DEMetro_Z |
0.3
|
-3.706
|
0.00347
|
-1.070
|
| HMC_vs_DEMetro_Z |
0.5
|
-1.399
|
0.189
|
-0.404
|
| HMC_vs_DEMetro_Z |
0.9
|
-1.730
|
0.111
|
-0.500
|
| HMC_vs_DEMetro_Z |
0.95
|
-1.559
|
0.147
|
-0.450
|
| HMC_vs_DEMetro_Z |
0.99
|
-2.128
|
0.0568
|
-0.614
|
| Metro_vs_SMC |
0.0
|
5.828
|
0.000114
|
1.682
|
| Metro_vs_SMC |
0.3
|
2.709
|
0.0203
|
0.782
|
| Metro_vs_SMC |
0.5
|
0.956
|
0.36
|
0.276
|
| Metro_vs_SMC |
0.9
|
2.337
|
0.0394
|
0.675
|
| Metro_vs_SMC |
0.95
|
6.443
|
4.79e-05
|
1.860
|
| Metro_vs_SMC |
0.99
|
4.342
|
0.00117
|
1.253
|
| Metro_vs_DEMetro_Z |
0.0
|
-0.879
|
0.398
|
-0.254
|
| Metro_vs_DEMetro_Z |
0.3
|
-2.367
|
0.0374
|
-0.683
|
| Metro_vs_DEMetro_Z |
0.5
|
-1.497
|
0.162
|
-0.432
|
| Metro_vs_DEMetro_Z |
0.9
|
1.279
|
0.227
|
0.369
|
| Metro_vs_DEMetro_Z |
0.95
|
4.975
|
0.000418
|
1.436
|
| Metro_vs_DEMetro_Z |
0.99
|
3.634
|
0.00393
|
1.049
|
| HMC_vs_Metro |
0.0
|
-4.537
|
0.000847
|
-1.310
|
| HMC_vs_Metro |
0.3
|
-2.726
|
0.0197
|
-0.787
|
| HMC_vs_Metro |
0.5
|
0.664
|
0.521
|
0.192
|
| HMC_vs_Metro |
0.9
|
-2.244
|
0.0464
|
-0.648
|
| HMC_vs_Metro |
0.95
|
-6.168
|
7.03e-05
|
-1.780
|
| HMC_vs_Metro |
0.99
|
-4.254
|
0.00136
|
-1.228
|
| HMC_vs_SMC |
0.0
|
0.820
|
0.43
|
0.237
|
| HMC_vs_SMC |
0.3
|
-0.092
|
0.928
|
-0.027
|
| HMC_vs_SMC |
0.5
|
2.194
|
0.0506
|
0.633
|
| HMC_vs_SMC |
0.9
|
0.056
|
0.957
|
0.016
|
| HMC_vs_SMC |
0.95
|
1.190
|
0.259
|
0.344
|
| HMC_vs_SMC |
0.99
|
1.060
|
0.312
|
0.306
|
| DEMetro_Z_vs_SMC |
0.0
|
3.453
|
0.0054
|
0.997
|
| DEMetro_Z_vs_SMC |
0.3
|
3.692
|
0.00355
|
1.066
|
| DEMetro_Z_vs_SMC |
0.5
|
3.729
|
0.00333
|
1.076
|
| DEMetro_Z_vs_SMC |
0.9
|
1.889
|
0.0856
|
0.545
|
| DEMetro_Z_vs_SMC |
0.95
|
3.372
|
0.00623
|
0.974
|
| DEMetro_Z_vs_SMC |
0.99
|
6.481
|
4.55e-05
|
1.871
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.017 |
0.025 |
0.008 |
-0.984 |
| HMC |
0.3 |
0.018 |
0.020 |
0.009 |
-0.250 |
| HMC |
0.5 |
0.030 |
0.024 |
0.010 |
0.608 |
| HMC |
0.9 |
0.023 |
0.019 |
0.014 |
0.250 |
| HMC |
0.95 |
0.021 |
0.017 |
0.012 |
0.376 |
| HMC |
0.99 |
0.032 |
0.018 |
0.016 |
0.854 |
| SMC |
0.0 |
0.015 |
0.025 |
0.008 |
-1.288 |
| SMC |
0.3 |
0.018 |
0.020 |
0.009 |
-0.214 |
| SMC |
0.5 |
0.020 |
0.024 |
0.010 |
-0.412 |
| SMC |
0.9 |
0.023 |
0.019 |
0.014 |
0.226 |
| SMC |
0.95 |
0.015 |
0.017 |
0.012 |
-0.146 |
| SMC |
0.99 |
0.022 |
0.018 |
0.016 |
0.217 |
| Metro |
0.0 |
0.033 |
0.025 |
0.008 |
0.976 |
| Metro |
0.3 |
0.033 |
0.020 |
0.009 |
1.376 |
| Metro |
0.5 |
0.026 |
0.024 |
0.010 |
0.272 |
| Metro |
0.9 |
0.069 |
0.019 |
0.014 |
3.582 |
| Metro |
0.95 |
0.145 |
0.017 |
0.012 |
10.993 |
| Metro |
0.99 |
0.238 |
0.018 |
0.016 |
14.022 |
| DEMetro_Z |
0.0 |
0.040 |
0.025 |
0.008 |
1.853 |
| DEMetro_Z |
0.3 |
0.058 |
0.020 |
0.009 |
4.057 |
| DEMetro_Z |
0.5 |
0.040 |
0.024 |
0.010 |
1.685 |
| DEMetro_Z |
0.9 |
0.044 |
0.019 |
0.014 |
1.762 |
| DEMetro_Z |
0.95 |
0.037 |
0.017 |
0.012 |
1.696 |
| DEMetro_Z |
0.99 |
0.056 |
0.018 |
0.016 |
2.394 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
1.043 |
0.308 |
0.462 |
| HMC |
0.3 |
0.278 |
0.784 |
0.151 |
| HMC |
0.5 |
1.587 |
0.127 |
0.716 |
| HMC |
0.9 |
1.565 |
0.14 |
1.296 |
| HMC |
0.95 |
4.760 |
9.52e-05 |
2.010 |
| HMC |
0.99 |
-2.090 |
0.0486 |
-0.798 |
| SMC |
0.0 |
-0.307 |
0.762 |
-0.121 |
| SMC |
0.3 |
-0.797 |
0.434 |
-0.339 |
| SMC |
0.5 |
-0.606 |
0.552 |
-0.214 |
| SMC |
0.9 |
0.425 |
0.675 |
0.191 |
| SMC |
0.95 |
0.812 |
0.426 |
0.394 |
| SMC |
0.99 |
-2.120 |
0.0466 |
-0.758 |
| Metro |
0.0 |
1.958 |
0.0692 |
1.442 |
| Metro |
0.3 |
3.448 |
0.00284 |
1.917 |
| Metro |
0.5 |
3.377 |
0.003 |
1.668 |
| Metro |
0.9 |
2.887 |
0.00985 |
1.630 |
| Metro |
0.95 |
5.064 |
0.000253 |
6.019 |
| Metro |
0.99 |
2.917 |
0.0138 |
11.062 |
| DEMetro_Z |
0.0 |
3.326 |
0.00378 |
1.877 |
| DEMetro_Z |
0.3 |
2.143 |
0.0478 |
1.407 |
| DEMetro_Z |
0.5 |
2.653 |
0.0178 |
1.844 |
| DEMetro_Z |
0.9 |
1.852 |
0.0846 |
1.445 |
| DEMetro_Z |
0.95 |
0.972 |
0.346 |
0.660 |
| DEMetro_Z |
0.99 |
0.720 |
0.482 |
0.491 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0.0
|
1.296
|
0.222
|
0.374
|
| HMC_vs_SMC |
0.3
|
1.190
|
0.259
|
0.344
|
| HMC_vs_SMC |
0.5
|
2.494
|
0.0298
|
0.720
|
| HMC_vs_SMC |
0.9
|
1.278
|
0.228
|
0.369
|
| HMC_vs_SMC |
0.95
|
2.937
|
0.0135
|
0.848
|
| HMC_vs_SMC |
0.99
|
-0.105
|
0.918
|
-0.030
|
| Metro_vs_DEMetro_Z |
0.0
|
-0.702
|
0.497
|
-0.203
|
| Metro_vs_DEMetro_Z |
0.3
|
0.833
|
0.423
|
0.240
|
| Metro_vs_DEMetro_Z |
0.5
|
-0.319
|
0.756
|
-0.092
|
| Metro_vs_DEMetro_Z |
0.9
|
0.233
|
0.82
|
0.067
|
| Metro_vs_DEMetro_Z |
0.95
|
4.911
|
0.000463
|
1.418
|
| Metro_vs_DEMetro_Z |
0.99
|
2.558
|
0.0266
|
0.738
|
| HMC_vs_Metro |
0.0
|
-1.351
|
0.204
|
-0.390
|
| HMC_vs_Metro |
0.3
|
-3.625
|
0.00399
|
-1.046
|
| HMC_vs_Metro |
0.5
|
-1.550
|
0.149
|
-0.447
|
| HMC_vs_Metro |
0.9
|
-0.311
|
0.762
|
-0.090
|
| HMC_vs_Metro |
0.95
|
-3.340
|
0.0066
|
-0.964
|
| HMC_vs_Metro |
0.99
|
-3.114
|
0.00986
|
-0.899
|
| HMC_vs_DEMetro_Z |
0.0
|
-2.757
|
0.0187
|
-0.796
|
| HMC_vs_DEMetro_Z |
0.3
|
-1.867
|
0.0888
|
-0.539
|
| HMC_vs_DEMetro_Z |
0.5
|
-1.629
|
0.132
|
-0.470
|
| HMC_vs_DEMetro_Z |
0.9
|
-0.128
|
0.901
|
-0.037
|
| HMC_vs_DEMetro_Z |
0.95
|
2.040
|
0.0661
|
0.589
|
| HMC_vs_DEMetro_Z |
0.99
|
-1.879
|
0.087
|
-0.542
|
| Metro_vs_SMC |
0.0
|
2.140
|
0.0556
|
0.618
|
| Metro_vs_SMC |
0.3
|
4.428
|
0.00101
|
1.278
|
| Metro_vs_SMC |
0.5
|
4.813
|
0.000542
|
1.389
|
| Metro_vs_SMC |
0.9
|
1.966
|
0.075
|
0.568
|
| Metro_vs_SMC |
0.95
|
4.444
|
0.000988
|
1.283
|
| Metro_vs_SMC |
0.99
|
3.156
|
0.00914
|
0.911
|
| DEMetro_Z_vs_SMC |
0.0
|
3.049
|
0.0111
|
0.880
|
| DEMetro_Z_vs_SMC |
0.3
|
2.756
|
0.0187
|
0.796
|
| DEMetro_Z_vs_SMC |
0.5
|
2.870
|
0.0152
|
0.828
|
| DEMetro_Z_vs_SMC |
0.9
|
1.323
|
0.213
|
0.382
|
| DEMetro_Z_vs_SMC |
0.95
|
0.440
|
0.668
|
0.127
|
| DEMetro_Z_vs_SMC |
0.99
|
1.745
|
0.109
|
0.504
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.036 |
0.030 |
0.013 |
0.462 |
| HMC |
0.3 |
0.032 |
0.029 |
0.015 |
0.151 |
| HMC |
0.5 |
0.031 |
0.021 |
0.013 |
0.716 |
| HMC |
0.9 |
0.051 |
0.028 |
0.018 |
1.296 |
| HMC |
0.95 |
0.062 |
0.021 |
0.020 |
2.010 |
| HMC |
0.99 |
0.023 |
0.037 |
0.018 |
-0.798 |
| SMC |
0.0 |
0.028 |
0.030 |
0.013 |
-0.121 |
| SMC |
0.3 |
0.024 |
0.029 |
0.015 |
-0.339 |
| SMC |
0.5 |
0.018 |
0.021 |
0.013 |
-0.214 |
| SMC |
0.9 |
0.032 |
0.028 |
0.018 |
0.191 |
| SMC |
0.95 |
0.029 |
0.021 |
0.020 |
0.394 |
| SMC |
0.99 |
0.024 |
0.037 |
0.018 |
-0.758 |
| Metro |
0.0 |
0.049 |
0.030 |
0.013 |
1.442 |
| Metro |
0.3 |
0.058 |
0.029 |
0.015 |
1.917 |
| Metro |
0.5 |
0.044 |
0.021 |
0.013 |
1.668 |
| Metro |
0.9 |
0.057 |
0.028 |
0.018 |
1.630 |
| Metro |
0.95 |
0.142 |
0.021 |
0.020 |
6.019 |
| Metro |
0.99 |
0.234 |
0.037 |
0.018 |
11.062 |
| DEMetro_Z |
0.0 |
0.055 |
0.030 |
0.013 |
1.877 |
| DEMetro_Z |
0.3 |
0.050 |
0.029 |
0.015 |
1.407 |
| DEMetro_Z |
0.5 |
0.046 |
0.021 |
0.013 |
1.844 |
| DEMetro_Z |
0.9 |
0.054 |
0.028 |
0.018 |
1.445 |
| DEMetro_Z |
0.95 |
0.034 |
0.021 |
0.020 |
0.660 |
| DEMetro_Z |
0.99 |
0.046 |
0.037 |
0.018 |
0.491 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
-2.926 |
0.00782 |
-1.183 |
| HMC |
0.3 |
0.082 |
0.935 |
0.033 |
| HMC |
0.5 |
2.109 |
0.048 |
1.071 |
| HMC |
0.9 |
2.218 |
0.0379 |
1.048 |
| HMC |
0.95 |
3.001 |
0.00668 |
1.323 |
| HMC |
0.99 |
1.701 |
0.109 |
1.182 |
| SMC |
0.0 |
-2.996 |
0.00716 |
-1.484 |
| SMC |
0.3 |
-0.172 |
0.865 |
-0.080 |
| SMC |
0.5 |
-0.416 |
0.682 |
-0.190 |
| SMC |
0.9 |
0.208 |
0.838 |
0.109 |
| SMC |
0.95 |
-0.368 |
0.717 |
-0.130 |
| SMC |
0.99 |
-0.545 |
0.592 |
-0.200 |
| Metro |
0.0 |
3.305 |
0.00509 |
2.623 |
| Metro |
0.3 |
4.205 |
0.000444 |
2.104 |
| Metro |
0.5 |
3.267 |
0.00435 |
1.865 |
| Metro |
0.9 |
3.736 |
0.00293 |
5.818 |
| Metro |
0.95 |
6.908 |
2.07e-05 |
13.862 |
| Metro |
0.99 |
6.278 |
5.75e-05 |
25.295 |
| DEMetro_Z |
0.0 |
3.798 |
0.00253 |
5.205 |
| DEMetro_Z |
0.3 |
4.776 |
0.000384 |
5.100 |
| DEMetro_Z |
0.5 |
6.921 |
1.38e-06 |
3.660 |
| DEMetro_Z |
0.9 |
3.058 |
0.00901 |
2.906 |
| DEMetro_Z |
0.95 |
4.239 |
0.000588 |
2.664 |
| DEMetro_Z |
0.99 |
6.471 |
3.95e-06 |
3.545 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0.0
|
-2.226
|
0.0479
|
-0.642
|
| Metro_vs_DEMetro_Z |
0.3
|
-2.678
|
0.0215
|
-0.773
|
| Metro_vs_DEMetro_Z |
0.5
|
-2.172
|
0.0526
|
-0.627
|
| Metro_vs_DEMetro_Z |
0.9
|
1.703
|
0.117
|
0.492
|
| Metro_vs_DEMetro_Z |
0.95
|
5.117
|
0.000335
|
1.477
|
| Metro_vs_DEMetro_Z |
0.99
|
5.418
|
0.000211
|
1.564
|
| DEMetro_Z_vs_SMC |
0.0
|
5.386
|
0.000221
|
1.555
|
| DEMetro_Z_vs_SMC |
0.3
|
4.474
|
0.00094
|
1.292
|
| DEMetro_Z_vs_SMC |
0.5
|
6.754
|
3.14e-05
|
1.950
|
| DEMetro_Z_vs_SMC |
0.9
|
2.777
|
0.018
|
0.802
|
| DEMetro_Z_vs_SMC |
0.95
|
6.409
|
5.01e-05
|
1.850
|
| DEMetro_Z_vs_SMC |
0.99
|
10.563
|
4.27e-07
|
3.049
|
| HMC_vs_DEMetro_Z |
0.0
|
-4.405
|
0.00105
|
-1.272
|
| HMC_vs_DEMetro_Z |
0.3
|
-4.402
|
0.00106
|
-1.271
|
| HMC_vs_DEMetro_Z |
0.5
|
-3.819
|
0.00285
|
-1.103
|
| HMC_vs_DEMetro_Z |
0.9
|
-1.779
|
0.103
|
-0.514
|
| HMC_vs_DEMetro_Z |
0.95
|
-1.981
|
0.0731
|
-0.572
|
| HMC_vs_DEMetro_Z |
0.99
|
-2.966
|
0.0128
|
-0.856
|
| HMC_vs_Metro |
0.0
|
-4.823
|
0.000533
|
-1.392
|
| HMC_vs_Metro |
0.3
|
-4.132
|
0.00167
|
-1.193
|
| HMC_vs_Metro |
0.5
|
-1.632
|
0.131
|
-0.471
|
| HMC_vs_Metro |
0.9
|
-2.786
|
0.0177
|
-0.804
|
| HMC_vs_Metro |
0.95
|
-6.103
|
7.7e-05
|
-1.762
|
| HMC_vs_Metro |
0.99
|
-6.167
|
7.03e-05
|
-1.780
|
| HMC_vs_SMC |
0.0
|
0.817
|
0.432
|
0.236
|
| HMC_vs_SMC |
0.3
|
0.300
|
0.77
|
0.086
|
| HMC_vs_SMC |
0.5
|
2.528
|
0.0281
|
0.730
|
| HMC_vs_SMC |
0.9
|
1.546
|
0.15
|
0.446
|
| HMC_vs_SMC |
0.95
|
3.473
|
0.00522
|
1.002
|
| HMC_vs_SMC |
0.99
|
1.957
|
0.0762
|
0.565
|
| Metro_vs_SMC |
0.0
|
5.465
|
0.000196
|
1.577
|
| Metro_vs_SMC |
0.3
|
3.834
|
0.00278
|
1.107
|
| Metro_vs_SMC |
0.5
|
3.136
|
0.00947
|
0.905
|
| Metro_vs_SMC |
0.9
|
3.264
|
0.00754
|
0.942
|
| Metro_vs_SMC |
0.95
|
7.119
|
1.94e-05
|
2.055
|
| Metro_vs_SMC |
0.99
|
6.327
|
5.62e-05
|
1.827
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.027 |
0.032 |
0.004 |
-1.183 |
| HMC |
0.3 |
0.029 |
0.029 |
0.007 |
0.033 |
| HMC |
0.5 |
0.035 |
0.028 |
0.006 |
1.071 |
| HMC |
0.9 |
0.037 |
0.027 |
0.009 |
1.048 |
| HMC |
0.95 |
0.037 |
0.026 |
0.009 |
1.323 |
| HMC |
0.99 |
0.038 |
0.027 |
0.009 |
1.182 |
| SMC |
0.0 |
0.026 |
0.032 |
0.004 |
-1.484 |
| SMC |
0.3 |
0.029 |
0.029 |
0.007 |
-0.080 |
| SMC |
0.5 |
0.027 |
0.028 |
0.006 |
-0.190 |
| SMC |
0.9 |
0.028 |
0.027 |
0.009 |
0.109 |
| SMC |
0.95 |
0.024 |
0.026 |
0.009 |
-0.130 |
| SMC |
0.99 |
0.026 |
0.027 |
0.009 |
-0.200 |
| Metro |
0.0 |
0.043 |
0.032 |
0.004 |
2.623 |
| Metro |
0.3 |
0.043 |
0.029 |
0.007 |
2.104 |
| Metro |
0.5 |
0.040 |
0.028 |
0.006 |
1.865 |
| Metro |
0.9 |
0.078 |
0.027 |
0.009 |
5.818 |
| Metro |
0.95 |
0.144 |
0.026 |
0.009 |
13.862 |
| Metro |
0.99 |
0.253 |
0.027 |
0.009 |
25.295 |
| DEMetro_Z |
0.0 |
0.054 |
0.032 |
0.004 |
5.205 |
| DEMetro_Z |
0.3 |
0.064 |
0.029 |
0.007 |
5.100 |
| DEMetro_Z |
0.5 |
0.051 |
0.028 |
0.006 |
3.660 |
| DEMetro_Z |
0.9 |
0.053 |
0.027 |
0.009 |
2.906 |
| DEMetro_Z |
0.95 |
0.048 |
0.026 |
0.009 |
2.664 |
| DEMetro_Z |
0.99 |
0.059 |
0.027 |
0.009 |
3.545 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
-2.392 |
0.0265 |
-0.864 |
| HMC |
0.3 |
0.234 |
0.817 |
0.096 |
| HMC |
0.5 |
2.115 |
0.0517 |
1.555 |
| HMC |
0.9 |
2.500 |
0.0219 |
1.333 |
| HMC |
0.95 |
2.833 |
0.00972 |
1.204 |
| HMC |
0.99 |
1.327 |
0.202 |
0.802 |
| SMC |
0.0 |
-2.966 |
0.00713 |
-1.211 |
| SMC |
0.3 |
-0.576 |
0.571 |
-0.276 |
| SMC |
0.5 |
-0.594 |
0.56 |
-0.377 |
| SMC |
0.9 |
0.486 |
0.633 |
0.262 |
| SMC |
0.95 |
-0.735 |
0.471 |
-0.267 |
| SMC |
0.99 |
-1.132 |
0.27 |
-0.429 |
| Metro |
0.0 |
3.007 |
0.00763 |
1.709 |
| Metro |
0.3 |
3.602 |
0.00171 |
1.711 |
| Metro |
0.5 |
3.394 |
0.00405 |
2.495 |
| Metro |
0.9 |
4.915 |
0.000325 |
5.812 |
| Metro |
0.95 |
8.560 |
1.92e-06 |
12.138 |
| Metro |
0.99 |
7.762 |
7.57e-06 |
20.918 |
| DEMetro_Z |
0.0 |
2.867 |
0.0137 |
3.290 |
| DEMetro_Z |
0.3 |
3.805 |
0.00223 |
3.932 |
| DEMetro_Z |
0.5 |
5.411 |
0.000118 |
5.354 |
| DEMetro_Z |
0.9 |
3.248 |
0.00602 |
2.855 |
| DEMetro_Z |
0.95 |
4.159 |
0.000582 |
2.315 |
| DEMetro_Z |
0.99 |
4.893 |
0.000135 |
2.931 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0.0
|
4.115
|
0.00171
|
1.188
|
| DEMetro_Z_vs_SMC |
0.3
|
3.707
|
0.00346
|
1.070
|
| DEMetro_Z_vs_SMC |
0.5
|
5.626
|
0.000154
|
1.624
|
| DEMetro_Z_vs_SMC |
0.9
|
2.725
|
0.0198
|
0.787
|
| DEMetro_Z_vs_SMC |
0.95
|
5.703
|
0.000138
|
1.646
|
| DEMetro_Z_vs_SMC |
0.99
|
7.808
|
8.22e-06
|
2.254
|
| HMC_vs_Metro |
0.0
|
-5.204
|
0.000293
|
-1.502
|
| HMC_vs_Metro |
0.3
|
-3.570
|
0.0044
|
-1.031
|
| HMC_vs_Metro |
0.5
|
-1.129
|
0.283
|
-0.326
|
| HMC_vs_Metro |
0.9
|
-3.367
|
0.00629
|
-0.972
|
| HMC_vs_Metro |
0.95
|
-7.382
|
1.39e-05
|
-2.131
|
| HMC_vs_Metro |
0.99
|
-7.698
|
9.4e-06
|
-2.222
|
| Metro_vs_DEMetro_Z |
0.0
|
-1.517
|
0.157
|
-0.438
|
| Metro_vs_DEMetro_Z |
0.3
|
-1.902
|
0.0836
|
-0.549
|
| Metro_vs_DEMetro_Z |
0.5
|
-2.023
|
0.0681
|
-0.584
|
| Metro_vs_DEMetro_Z |
0.9
|
2.401
|
0.0351
|
0.693
|
| Metro_vs_DEMetro_Z |
0.95
|
5.959
|
9.47e-05
|
1.720
|
| Metro_vs_DEMetro_Z |
0.99
|
6.772
|
3.06e-05
|
1.955
|
| HMC_vs_SMC |
0.0
|
1.181
|
0.263
|
0.341
|
| HMC_vs_SMC |
0.3
|
1.047
|
0.318
|
0.302
|
| HMC_vs_SMC |
0.5
|
2.425
|
0.0337
|
0.700
|
| HMC_vs_SMC |
0.9
|
1.685
|
0.12
|
0.487
|
| HMC_vs_SMC |
0.95
|
3.744
|
0.00324
|
1.081
|
| HMC_vs_SMC |
0.99
|
1.955
|
0.0765
|
0.564
|
| Metro_vs_SMC |
0.0
|
5.046
|
0.000375
|
1.457
|
| Metro_vs_SMC |
0.3
|
3.587
|
0.00426
|
1.036
|
| Metro_vs_SMC |
0.5
|
2.986
|
0.0124
|
0.862
|
| Metro_vs_SMC |
0.9
|
4.237
|
0.0014
|
1.223
|
| Metro_vs_SMC |
0.95
|
9.130
|
1.82e-06
|
2.636
|
| Metro_vs_SMC |
0.99
|
7.655
|
9.9e-06
|
2.210
|
| HMC_vs_DEMetro_Z |
0.0
|
-3.434
|
0.00558
|
-0.991
|
| HMC_vs_DEMetro_Z |
0.3
|
-3.314
|
0.0069
|
-0.957
|
| HMC_vs_DEMetro_Z |
0.5
|
-3.334
|
0.00667
|
-0.962
|
| HMC_vs_DEMetro_Z |
0.9
|
-1.649
|
0.127
|
-0.476
|
| HMC_vs_DEMetro_Z |
0.95
|
-1.923
|
0.0807
|
-0.555
|
| HMC_vs_DEMetro_Z |
0.99
|
-2.878
|
0.015
|
-0.831
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.013 |
0.016 |
0.004 |
-0.864 |
| HMC |
0.3 |
0.015 |
0.014 |
0.005 |
0.096 |
| HMC |
0.5 |
0.018 |
0.014 |
0.003 |
1.555 |
| HMC |
0.9 |
0.021 |
0.014 |
0.005 |
1.333 |
| HMC |
0.95 |
0.021 |
0.014 |
0.005 |
1.204 |
| HMC |
0.99 |
0.020 |
0.015 |
0.005 |
0.802 |
| SMC |
0.0 |
0.012 |
0.016 |
0.004 |
-1.211 |
| SMC |
0.3 |
0.013 |
0.014 |
0.005 |
-0.276 |
| SMC |
0.5 |
0.013 |
0.014 |
0.003 |
-0.377 |
| SMC |
0.9 |
0.015 |
0.014 |
0.005 |
0.262 |
| SMC |
0.95 |
0.013 |
0.014 |
0.005 |
-0.267 |
| SMC |
0.99 |
0.013 |
0.015 |
0.005 |
-0.429 |
| Metro |
0.0 |
0.022 |
0.016 |
0.004 |
1.709 |
| Metro |
0.3 |
0.022 |
0.014 |
0.005 |
1.711 |
| Metro |
0.5 |
0.020 |
0.014 |
0.003 |
2.495 |
| Metro |
0.9 |
0.045 |
0.014 |
0.005 |
5.812 |
| Metro |
0.95 |
0.079 |
0.014 |
0.005 |
12.138 |
| Metro |
0.99 |
0.130 |
0.015 |
0.005 |
20.918 |
| DEMetro_Z |
0.0 |
0.028 |
0.016 |
0.004 |
3.290 |
| DEMetro_Z |
0.3 |
0.033 |
0.014 |
0.005 |
3.932 |
| DEMetro_Z |
0.5 |
0.028 |
0.014 |
0.003 |
5.354 |
| DEMetro_Z |
0.9 |
0.029 |
0.014 |
0.005 |
2.855 |
| DEMetro_Z |
0.95 |
0.027 |
0.014 |
0.005 |
2.315 |
| DEMetro_Z |
0.99 |
0.032 |
0.015 |
0.005 |
2.931 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
R Hat (scatter)
Mode Transitions
One Chain results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
-0.858 |
0.4 |
-0.351 |
| HMC |
0.3 |
-0.726 |
0.476 |
-0.267 |
| HMC |
0.5 |
-0.340 |
0.738 |
-0.161 |
| HMC |
0.9 |
-0.326 |
0.748 |
-0.149 |
| HMC |
0.95 |
1.462 |
0.166 |
1.196 |
| HMC |
0.99 |
1.930 |
0.0672 |
0.886 |
| SMC |
0.0 |
-1.006 |
0.326 |
-0.494 |
| SMC |
0.3 |
-0.460 |
0.65 |
-0.188 |
| SMC |
0.5 |
-0.301 |
0.766 |
-0.124 |
| SMC |
0.9 |
-0.061 |
0.952 |
-0.030 |
| SMC |
0.95 |
0.901 |
0.378 |
0.421 |
| SMC |
0.99 |
0.049 |
0.961 |
0.019 |
| Metro |
0.0 |
2.132 |
0.0501 |
1.574 |
| Metro |
0.3 |
3.047 |
0.00784 |
2.061 |
| Metro |
0.5 |
1.401 |
0.183 |
1.132 |
| Metro |
0.9 |
4.592 |
0.000549 |
5.095 |
| Metro |
0.95 |
3.233 |
0.00761 |
6.764 |
| Metro |
0.99 |
5.860 |
0.000105 |
24.862 |
| DEMetro_Z |
0.0 |
1.607 |
0.128 |
1.077 |
| DEMetro_Z |
0.3 |
1.630 |
0.122 |
1.041 |
| DEMetro_Z |
0.5 |
2.395 |
0.0309 |
1.909 |
| DEMetro_Z |
0.9 |
2.256 |
0.0391 |
1.586 |
| DEMetro_Z |
0.95 |
1.947 |
0.0744 |
2.244 |
| DEMetro_Z |
0.99 |
1.361 |
0.189 |
0.704 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0.0
|
-2.043
|
0.0657
|
-0.590
|
| HMC_vs_DEMetro_Z |
0.3
|
-1.817
|
0.0966
|
-0.524
|
| HMC_vs_DEMetro_Z |
0.5
|
-2.846
|
0.0159
|
-0.822
|
| HMC_vs_DEMetro_Z |
0.9
|
-2.371
|
0.0371
|
-0.684
|
| HMC_vs_DEMetro_Z |
0.95
|
-0.764
|
0.461
|
-0.221
|
| HMC_vs_DEMetro_Z |
0.99
|
0.297
|
0.772
|
0.086
|
| Metro_vs_SMC |
0.0
|
3.702
|
0.00349
|
1.069
|
| Metro_vs_SMC |
0.3
|
3.252
|
0.00771
|
0.939
|
| Metro_vs_SMC |
0.5
|
2.053
|
0.0646
|
0.593
|
| Metro_vs_SMC |
0.9
|
5.125
|
0.000331
|
1.479
|
| Metro_vs_SMC |
0.95
|
3.037
|
0.0113
|
0.877
|
| Metro_vs_SMC |
0.99
|
6.041
|
8.41e-05
|
1.744
|
| Metro_vs_DEMetro_Z |
0.0
|
0.469
|
0.649
|
0.135
|
| Metro_vs_DEMetro_Z |
0.3
|
1.199
|
0.256
|
0.346
|
| Metro_vs_DEMetro_Z |
0.5
|
-0.743
|
0.473
|
-0.214
|
| Metro_vs_DEMetro_Z |
0.9
|
3.422
|
0.0057
|
0.988
|
| Metro_vs_DEMetro_Z |
0.95
|
1.691
|
0.119
|
0.488
|
| Metro_vs_DEMetro_Z |
0.99
|
5.795
|
0.00012
|
1.673
|
| HMC_vs_Metro |
0.0
|
-3.184
|
0.0087
|
-0.919
|
| HMC_vs_Metro |
0.3
|
-3.514
|
0.00485
|
-1.014
|
| HMC_vs_Metro |
0.5
|
-1.612
|
0.135
|
-0.465
|
| HMC_vs_Metro |
0.9
|
-4.283
|
0.00129
|
-1.236
|
| HMC_vs_Metro |
0.95
|
-2.312
|
0.0412
|
-0.667
|
| HMC_vs_Metro |
0.99
|
-5.487
|
0.00019
|
-1.584
|
| HMC_vs_SMC |
0.0
|
0.444
|
0.666
|
0.128
|
| HMC_vs_SMC |
0.3
|
-0.225
|
0.826
|
-0.065
|
| HMC_vs_SMC |
0.5
|
-0.087
|
0.932
|
-0.025
|
| HMC_vs_SMC |
0.9
|
-0.210
|
0.837
|
-0.061
|
| HMC_vs_SMC |
0.95
|
1.332
|
0.21
|
0.385
|
| HMC_vs_SMC |
0.99
|
1.814
|
0.097
|
0.524
|
| DEMetro_Z_vs_SMC |
0.0
|
2.139
|
0.0557
|
0.618
|
| DEMetro_Z_vs_SMC |
0.3
|
2.154
|
0.0543
|
0.622
|
| DEMetro_Z_vs_SMC |
0.5
|
2.293
|
0.0426
|
0.662
|
| DEMetro_Z_vs_SMC |
0.9
|
2.570
|
0.026
|
0.742
|
| DEMetro_Z_vs_SMC |
0.95
|
1.489
|
0.165
|
0.430
|
| DEMetro_Z_vs_SMC |
0.99
|
1.303
|
0.219
|
0.376
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.022 |
0.025 |
0.008 |
-0.351 |
| HMC |
0.3 |
0.018 |
0.020 |
0.009 |
-0.267 |
| HMC |
0.5 |
0.022 |
0.024 |
0.010 |
-0.161 |
| HMC |
0.9 |
0.017 |
0.019 |
0.014 |
-0.149 |
| HMC |
0.95 |
0.031 |
0.017 |
0.012 |
1.196 |
| HMC |
0.99 |
0.032 |
0.018 |
0.016 |
0.886 |
| SMC |
0.0 |
0.021 |
0.025 |
0.008 |
-0.494 |
| SMC |
0.3 |
0.019 |
0.020 |
0.009 |
-0.188 |
| SMC |
0.5 |
0.023 |
0.024 |
0.010 |
-0.124 |
| SMC |
0.9 |
0.019 |
0.019 |
0.014 |
-0.030 |
| SMC |
0.95 |
0.022 |
0.017 |
0.012 |
0.421 |
| SMC |
0.99 |
0.018 |
0.018 |
0.016 |
0.019 |
| Metro |
0.0 |
0.038 |
0.025 |
0.008 |
1.574 |
| Metro |
0.3 |
0.040 |
0.020 |
0.009 |
2.061 |
| Metro |
0.5 |
0.035 |
0.024 |
0.010 |
1.132 |
| Metro |
0.9 |
0.089 |
0.019 |
0.014 |
5.095 |
| Metro |
0.95 |
0.096 |
0.017 |
0.012 |
6.764 |
| Metro |
0.99 |
0.407 |
0.018 |
0.016 |
24.862 |
| DEMetro_Z |
0.0 |
0.034 |
0.025 |
0.008 |
1.077 |
| DEMetro_Z |
0.3 |
0.030 |
0.020 |
0.009 |
1.041 |
| DEMetro_Z |
0.5 |
0.042 |
0.024 |
0.010 |
1.909 |
| DEMetro_Z |
0.9 |
0.041 |
0.019 |
0.014 |
1.586 |
| DEMetro_Z |
0.95 |
0.043 |
0.017 |
0.012 |
2.244 |
| DEMetro_Z |
0.99 |
0.029 |
0.018 |
0.016 |
0.704 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
0.761 |
0.455 |
0.368 |
| HMC |
0.3 |
0.058 |
0.955 |
0.022 |
| HMC |
0.5 |
0.225 |
0.824 |
0.098 |
| HMC |
0.9 |
1.975 |
0.0666 |
1.388 |
| HMC |
0.95 |
2.033 |
0.0572 |
1.145 |
| HMC |
0.99 |
-0.523 |
0.607 |
-0.272 |
| SMC |
0.0 |
-0.114 |
0.911 |
-0.050 |
| SMC |
0.3 |
0.639 |
0.529 |
0.248 |
| SMC |
0.5 |
2.338 |
0.0303 |
1.205 |
| SMC |
0.9 |
-1.770 |
0.0923 |
-0.623 |
| SMC |
0.95 |
1.288 |
0.211 |
0.507 |
| SMC |
0.99 |
-2.291 |
0.0319 |
-0.908 |
| Metro |
0.0 |
2.006 |
0.0611 |
1.210 |
| Metro |
0.3 |
0.780 |
0.446 |
0.457 |
| Metro |
0.5 |
2.567 |
0.0223 |
2.098 |
| Metro |
0.9 |
3.087 |
0.00642 |
1.756 |
| Metro |
0.95 |
5.391 |
0.00014 |
6.083 |
| Metro |
0.99 |
4.522 |
0.000826 |
12.858 |
| DEMetro_Z |
0.0 |
3.678 |
0.00249 |
3.046 |
| DEMetro_Z |
0.3 |
2.219 |
0.041 |
1.415 |
| DEMetro_Z |
0.5 |
4.867 |
0.000147 |
2.958 |
| DEMetro_Z |
0.9 |
2.472 |
0.0259 |
1.804 |
| DEMetro_Z |
0.95 |
2.293 |
0.0368 |
1.681 |
| DEMetro_Z |
0.99 |
0.849 |
0.408 |
0.508 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0.0
|
0.824
|
0.427
|
0.238
|
| HMC_vs_SMC |
0.3
|
-0.539
|
0.601
|
-0.155
|
| HMC_vs_SMC |
0.5
|
-1.903
|
0.0836
|
-0.549
|
| HMC_vs_SMC |
0.9
|
2.762
|
0.0185
|
0.797
|
| HMC_vs_SMC |
0.95
|
1.391
|
0.192
|
0.402
|
| HMC_vs_SMC |
0.99
|
1.499
|
0.162
|
0.433
|
| Metro_vs_DEMetro_Z |
0.0
|
-2.069
|
0.0628
|
-0.597
|
| Metro_vs_DEMetro_Z |
0.3
|
-1.020
|
0.33
|
-0.294
|
| Metro_vs_DEMetro_Z |
0.5
|
-1.076
|
0.305
|
-0.311
|
| Metro_vs_DEMetro_Z |
0.9
|
-0.092
|
0.928
|
-0.027
|
| Metro_vs_DEMetro_Z |
0.95
|
3.059
|
0.0109
|
0.883
|
| Metro_vs_DEMetro_Z |
0.99
|
4.270
|
0.00132
|
1.233
|
| HMC_vs_Metro |
0.0
|
-1.147
|
0.276
|
-0.331
|
| HMC_vs_Metro |
0.3
|
-0.857
|
0.41
|
-0.247
|
| HMC_vs_Metro |
0.5
|
-2.278
|
0.0437
|
-0.658
|
| HMC_vs_Metro |
0.9
|
-0.565
|
0.584
|
-0.163
|
| HMC_vs_Metro |
0.95
|
-4.368
|
0.00112
|
-1.261
|
| HMC_vs_Metro |
0.99
|
-4.666
|
0.000687
|
-1.347
|
| HMC_vs_DEMetro_Z |
0.0
|
-3.351
|
0.00647
|
-0.967
|
| HMC_vs_DEMetro_Z |
0.3
|
-2.362
|
0.0377
|
-0.682
|
| HMC_vs_DEMetro_Z |
0.5
|
-4.492
|
0.000913
|
-1.297
|
| HMC_vs_DEMetro_Z |
0.9
|
-0.458
|
0.656
|
-0.132
|
| HMC_vs_DEMetro_Z |
0.95
|
-0.749
|
0.469
|
-0.216
|
| HMC_vs_DEMetro_Z |
0.99
|
-1.071
|
0.307
|
-0.309
|
| Metro_vs_SMC |
0.0
|
1.762
|
0.106
|
0.509
|
| Metro_vs_SMC |
0.3
|
0.419
|
0.683
|
0.121
|
| Metro_vs_SMC |
0.5
|
1.147
|
0.276
|
0.331
|
| Metro_vs_SMC |
0.9
|
4.033
|
0.00197
|
1.164
|
| Metro_vs_SMC |
0.95
|
5.240
|
0.000277
|
1.513
|
| Metro_vs_SMC |
0.99
|
4.689
|
0.000662
|
1.354
|
| DEMetro_Z_vs_SMC |
0.0
|
3.502
|
0.00495
|
1.011
|
| DEMetro_Z_vs_SMC |
0.3
|
1.854
|
0.0907
|
0.535
|
| DEMetro_Z_vs_SMC |
0.5
|
2.356
|
0.038
|
0.680
|
| DEMetro_Z_vs_SMC |
0.9
|
3.355
|
0.00642
|
0.969
|
| DEMetro_Z_vs_SMC |
0.95
|
1.680
|
0.121
|
0.485
|
| DEMetro_Z_vs_SMC |
0.99
|
2.169
|
0.0529
|
0.626
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.035 |
0.030 |
0.013 |
0.368 |
| HMC |
0.3 |
0.030 |
0.029 |
0.015 |
0.022 |
| HMC |
0.5 |
0.023 |
0.021 |
0.013 |
0.098 |
| HMC |
0.9 |
0.053 |
0.028 |
0.018 |
1.388 |
| HMC |
0.95 |
0.044 |
0.021 |
0.020 |
1.145 |
| HMC |
0.99 |
0.033 |
0.037 |
0.018 |
-0.272 |
| SMC |
0.0 |
0.029 |
0.030 |
0.013 |
-0.050 |
| SMC |
0.3 |
0.033 |
0.029 |
0.015 |
0.248 |
| SMC |
0.5 |
0.037 |
0.021 |
0.013 |
1.205 |
| SMC |
0.9 |
0.017 |
0.028 |
0.018 |
-0.623 |
| SMC |
0.95 |
0.031 |
0.021 |
0.020 |
0.507 |
| SMC |
0.99 |
0.021 |
0.037 |
0.018 |
-0.908 |
| Metro |
0.0 |
0.046 |
0.030 |
0.013 |
1.210 |
| Metro |
0.3 |
0.036 |
0.029 |
0.015 |
0.457 |
| Metro |
0.5 |
0.049 |
0.021 |
0.013 |
2.098 |
| Metro |
0.9 |
0.059 |
0.028 |
0.018 |
1.756 |
| Metro |
0.95 |
0.144 |
0.021 |
0.020 |
6.083 |
| Metro |
0.99 |
0.266 |
0.037 |
0.018 |
12.858 |
| DEMetro_Z |
0.0 |
0.070 |
0.030 |
0.013 |
3.046 |
| DEMetro_Z |
0.3 |
0.050 |
0.029 |
0.015 |
1.415 |
| DEMetro_Z |
0.5 |
0.061 |
0.021 |
0.013 |
2.958 |
| DEMetro_Z |
0.9 |
0.060 |
0.028 |
0.018 |
1.804 |
| DEMetro_Z |
0.95 |
0.055 |
0.021 |
0.020 |
1.681 |
| DEMetro_Z |
0.99 |
0.046 |
0.037 |
0.018 |
0.508 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
-0.551 |
0.588 |
-0.274 |
| HMC |
0.3 |
-0.352 |
0.728 |
-0.125 |
| HMC |
0.5 |
0.692 |
0.496 |
0.289 |
| HMC |
0.9 |
1.398 |
0.179 |
0.753 |
| HMC |
0.95 |
2.046 |
0.0611 |
1.926 |
| HMC |
0.99 |
2.583 |
0.0176 |
1.246 |
| SMC |
0.0 |
-1.021 |
0.321 |
-0.583 |
| SMC |
0.3 |
-0.521 |
0.607 |
-0.198 |
| SMC |
0.5 |
0.448 |
0.659 |
0.207 |
| SMC |
0.9 |
-0.163 |
0.872 |
-0.084 |
| SMC |
0.95 |
0.759 |
0.456 |
0.329 |
| SMC |
0.99 |
-0.478 |
0.637 |
-0.177 |
| Metro |
0.0 |
4.386 |
0.000497 |
3.025 |
| Metro |
0.3 |
4.243 |
0.000538 |
2.527 |
| Metro |
0.5 |
3.125 |
0.008 |
3.047 |
| Metro |
0.9 |
5.081 |
0.000273 |
7.149 |
| Metro |
0.95 |
5.438 |
0.000173 |
10.155 |
| Metro |
0.99 |
7.201 |
1.7e-05 |
42.055 |
| DEMetro_Z |
0.0 |
5.503 |
0.000101 |
5.459 |
| DEMetro_Z |
0.3 |
4.286 |
0.000495 |
2.572 |
| DEMetro_Z |
0.5 |
5.511 |
6.92e-05 |
4.297 |
| DEMetro_Z |
0.9 |
4.905 |
0.000138 |
3.008 |
| DEMetro_Z |
0.95 |
3.433 |
0.00462 |
3.757 |
| DEMetro_Z |
0.99 |
2.719 |
0.0152 |
1.788 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0.0
|
-1.940
|
0.0784
|
-0.560
|
| Metro_vs_DEMetro_Z |
0.3
|
-0.060
|
0.953
|
-0.017
|
| Metro_vs_DEMetro_Z |
0.5
|
-0.981
|
0.348
|
-0.283
|
| Metro_vs_DEMetro_Z |
0.9
|
3.142
|
0.00937
|
0.907
|
| Metro_vs_DEMetro_Z |
0.95
|
2.893
|
0.0146
|
0.835
|
| Metro_vs_DEMetro_Z |
0.99
|
6.832
|
2.83e-05
|
1.972
|
| DEMetro_Z_vs_SMC |
0.0
|
5.112
|
0.000338
|
1.476
|
| DEMetro_Z_vs_SMC |
0.3
|
5.701
|
0.000138
|
1.646
|
| DEMetro_Z_vs_SMC |
0.5
|
4.584
|
0.000785
|
1.323
|
| DEMetro_Z_vs_SMC |
0.9
|
4.850
|
0.000511
|
1.400
|
| DEMetro_Z_vs_SMC |
0.95
|
3.159
|
0.0091
|
0.912
|
| DEMetro_Z_vs_SMC |
0.99
|
2.669
|
0.0218
|
0.770
|
| HMC_vs_DEMetro_Z |
0.0
|
-5.175
|
0.000306
|
-1.494
|
| HMC_vs_DEMetro_Z |
0.3
|
-4.287
|
0.00128
|
-1.238
|
| HMC_vs_DEMetro_Z |
0.5
|
-5.421
|
0.00021
|
-1.565
|
| HMC_vs_DEMetro_Z |
0.9
|
-4.440
|
0.000995
|
-1.282
|
| HMC_vs_DEMetro_Z |
0.95
|
-1.352
|
0.203
|
-0.390
|
| HMC_vs_DEMetro_Z |
0.99
|
-0.757
|
0.465
|
-0.218
|
| HMC_vs_Metro |
0.0
|
-4.803
|
0.000551
|
-1.387
|
| HMC_vs_Metro |
0.3
|
-5.287
|
0.000258
|
-1.526
|
| HMC_vs_Metro |
0.5
|
-2.949
|
0.0132
|
-0.851
|
| HMC_vs_Metro |
0.9
|
-4.364
|
0.00113
|
-1.260
|
| HMC_vs_Metro |
0.95
|
-3.937
|
0.00232
|
-1.136
|
| HMC_vs_Metro |
0.99
|
-6.917
|
2.53e-05
|
-1.997
|
| HMC_vs_SMC |
0.0
|
0.595
|
0.564
|
0.172
|
| HMC_vs_SMC |
0.3
|
0.211
|
0.837
|
0.061
|
| HMC_vs_SMC |
0.5
|
0.216
|
0.833
|
0.062
|
| HMC_vs_SMC |
0.9
|
1.499
|
0.162
|
0.433
|
| HMC_vs_SMC |
0.95
|
2.226
|
0.0479
|
0.642
|
| HMC_vs_SMC |
0.99
|
2.845
|
0.016
|
0.821
|
| Metro_vs_SMC |
0.0
|
9.507
|
1.22e-06
|
2.744
|
| Metro_vs_SMC |
0.3
|
4.832
|
0.000526
|
1.395
|
| Metro_vs_SMC |
0.5
|
3.299
|
0.00709
|
0.952
|
| Metro_vs_SMC |
0.9
|
5.331
|
0.000241
|
1.539
|
| Metro_vs_SMC |
0.95
|
5.561
|
0.00017
|
1.605
|
| Metro_vs_SMC |
0.99
|
7.346
|
1.46e-05
|
2.121
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.031 |
0.032 |
0.004 |
-0.274 |
| HMC |
0.3 |
0.028 |
0.029 |
0.007 |
-0.125 |
| HMC |
0.5 |
0.030 |
0.028 |
0.006 |
0.289 |
| HMC |
0.9 |
0.034 |
0.027 |
0.009 |
0.753 |
| HMC |
0.95 |
0.042 |
0.026 |
0.009 |
1.926 |
| HMC |
0.99 |
0.039 |
0.027 |
0.009 |
1.246 |
| SMC |
0.0 |
0.030 |
0.032 |
0.004 |
-0.583 |
| SMC |
0.3 |
0.028 |
0.029 |
0.007 |
-0.198 |
| SMC |
0.5 |
0.030 |
0.028 |
0.006 |
0.207 |
| SMC |
0.9 |
0.027 |
0.027 |
0.009 |
-0.084 |
| SMC |
0.95 |
0.028 |
0.026 |
0.009 |
0.329 |
| SMC |
0.99 |
0.026 |
0.027 |
0.009 |
-0.177 |
| Metro |
0.0 |
0.045 |
0.032 |
0.004 |
3.025 |
| Metro |
0.3 |
0.046 |
0.029 |
0.007 |
2.527 |
| Metro |
0.5 |
0.047 |
0.028 |
0.006 |
3.047 |
| Metro |
0.9 |
0.090 |
0.027 |
0.009 |
7.149 |
| Metro |
0.95 |
0.112 |
0.026 |
0.009 |
10.155 |
| Metro |
0.99 |
0.402 |
0.027 |
0.009 |
42.055 |
| DEMetro_Z |
0.0 |
0.055 |
0.032 |
0.004 |
5.459 |
| DEMetro_Z |
0.3 |
0.047 |
0.029 |
0.007 |
2.572 |
| DEMetro_Z |
0.5 |
0.055 |
0.028 |
0.006 |
4.297 |
| DEMetro_Z |
0.9 |
0.054 |
0.027 |
0.009 |
3.008 |
| DEMetro_Z |
0.95 |
0.058 |
0.026 |
0.009 |
3.757 |
| DEMetro_Z |
0.99 |
0.043 |
0.027 |
0.009 |
1.788 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
-0.575 |
0.571 |
-0.257 |
| HMC |
0.3 |
-0.766 |
0.452 |
-0.272 |
| HMC |
0.5 |
0.858 |
0.402 |
0.477 |
| HMC |
0.9 |
1.591 |
0.132 |
1.064 |
| HMC |
0.95 |
1.761 |
0.1 |
1.436 |
| HMC |
0.99 |
1.629 |
0.118 |
0.686 |
| SMC |
0.0 |
-0.763 |
0.454 |
-0.368 |
| SMC |
0.3 |
-1.007 |
0.325 |
-0.392 |
| SMC |
0.5 |
1.010 |
0.329 |
0.787 |
| SMC |
0.9 |
0.064 |
0.949 |
0.032 |
| SMC |
0.95 |
0.302 |
0.766 |
0.139 |
| SMC |
0.99 |
-1.619 |
0.124 |
-0.536 |
| Metro |
0.0 |
2.837 |
0.0121 |
1.911 |
| Metro |
0.3 |
3.572 |
0.00227 |
2.084 |
| Metro |
0.5 |
3.233 |
0.00727 |
4.776 |
| Metro |
0.9 |
5.715 |
7.37e-05 |
5.862 |
| Metro |
0.95 |
5.909 |
7.43e-05 |
8.642 |
| Metro |
0.99 |
7.100 |
1.93e-05 |
36.245 |
| DEMetro_Z |
0.0 |
4.305 |
0.000663 |
3.272 |
| DEMetro_Z |
0.3 |
3.044 |
0.00687 |
1.671 |
| DEMetro_Z |
0.5 |
5.929 |
4.32e-05 |
5.365 |
| DEMetro_Z |
0.9 |
4.740 |
0.000234 |
3.202 |
| DEMetro_Z |
0.95 |
3.102 |
0.00771 |
2.497 |
| DEMetro_Z |
0.99 |
2.317 |
0.0335 |
1.430 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0.0
|
4.091
|
0.00179
|
1.181
|
| DEMetro_Z_vs_SMC |
0.3
|
4.124
|
0.00169
|
1.191
|
| DEMetro_Z_vs_SMC |
0.5
|
3.476
|
0.00518
|
1.004
|
| DEMetro_Z_vs_SMC |
0.9
|
4.523
|
0.000868
|
1.306
|
| DEMetro_Z_vs_SMC |
0.95
|
2.927
|
0.0138
|
0.845
|
| DEMetro_Z_vs_SMC |
0.99
|
2.952
|
0.0132
|
0.852
|
| HMC_vs_Metro |
0.0
|
-3.266
|
0.00752
|
-0.943
|
| HMC_vs_Metro |
0.3
|
-5.411
|
0.000213
|
-1.562
|
| HMC_vs_Metro |
0.5
|
-3.335
|
0.00665
|
-0.963
|
| HMC_vs_Metro |
0.9
|
-4.795
|
0.000558
|
-1.384
|
| HMC_vs_Metro |
0.95
|
-4.507
|
0.000891
|
-1.301
|
| HMC_vs_Metro |
0.99
|
-7.057
|
2.11e-05
|
-2.037
|
| Metro_vs_DEMetro_Z |
0.0
|
-1.591
|
0.14
|
-0.459
|
| Metro_vs_DEMetro_Z |
0.3
|
0.548
|
0.595
|
0.158
|
| Metro_vs_DEMetro_Z |
0.5
|
-0.302
|
0.768
|
-0.087
|
| Metro_vs_DEMetro_Z |
0.9
|
2.858
|
0.0156
|
0.825
|
| Metro_vs_DEMetro_Z |
0.95
|
4.004
|
0.00207
|
1.156
|
| Metro_vs_DEMetro_Z |
0.99
|
6.750
|
3.16e-05
|
1.948
|
| HMC_vs_SMC |
0.0
|
0.292
|
0.776
|
0.084
|
| HMC_vs_SMC |
0.3
|
0.355
|
0.729
|
0.103
|
| HMC_vs_SMC |
0.5
|
-0.506
|
0.623
|
-0.146
|
| HMC_vs_SMC |
0.9
|
1.550
|
0.149
|
0.448
|
| HMC_vs_SMC |
0.95
|
1.750
|
0.108
|
0.505
|
| HMC_vs_SMC |
0.99
|
3.100
|
0.0101
|
0.895
|
| Metro_vs_SMC |
0.0
|
5.374
|
0.000225
|
1.551
|
| Metro_vs_SMC |
0.3
|
4.296
|
0.00126
|
1.240
|
| Metro_vs_SMC |
0.5
|
3.418
|
0.00574
|
0.987
|
| Metro_vs_SMC |
0.9
|
6.664
|
3.54e-05
|
1.924
|
| Metro_vs_SMC |
0.95
|
6.156
|
7.15e-05
|
1.777
|
| Metro_vs_SMC |
0.99
|
7.204
|
1.74e-05
|
2.079
|
| HMC_vs_DEMetro_Z |
0.0
|
-4.274
|
0.00131
|
-1.234
|
| HMC_vs_DEMetro_Z |
0.3
|
-3.660
|
0.00375
|
-1.057
|
| HMC_vs_DEMetro_Z |
0.5
|
-4.838
|
0.000521
|
-1.397
|
| HMC_vs_DEMetro_Z |
0.9
|
-4.851
|
0.00051
|
-1.400
|
| HMC_vs_DEMetro_Z |
0.95
|
-0.997
|
0.34
|
-0.288
|
| HMC_vs_DEMetro_Z |
0.99
|
-1.129
|
0.283
|
-0.326
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.015 |
0.016 |
0.004 |
-0.257 |
| HMC |
0.3 |
0.013 |
0.014 |
0.005 |
-0.272 |
| HMC |
0.5 |
0.015 |
0.014 |
0.003 |
0.477 |
| HMC |
0.9 |
0.019 |
0.014 |
0.005 |
1.064 |
| HMC |
0.95 |
0.022 |
0.014 |
0.005 |
1.436 |
| HMC |
0.99 |
0.019 |
0.015 |
0.005 |
0.686 |
| SMC |
0.0 |
0.015 |
0.016 |
0.004 |
-0.368 |
| SMC |
0.3 |
0.013 |
0.014 |
0.005 |
-0.392 |
| SMC |
0.5 |
0.016 |
0.014 |
0.003 |
0.787 |
| SMC |
0.9 |
0.014 |
0.014 |
0.005 |
0.032 |
| SMC |
0.95 |
0.015 |
0.014 |
0.005 |
0.139 |
| SMC |
0.99 |
0.013 |
0.015 |
0.005 |
-0.536 |
| Metro |
0.0 |
0.023 |
0.016 |
0.004 |
1.911 |
| Metro |
0.3 |
0.024 |
0.014 |
0.005 |
2.084 |
| Metro |
0.5 |
0.026 |
0.014 |
0.003 |
4.776 |
| Metro |
0.9 |
0.045 |
0.014 |
0.005 |
5.862 |
| Metro |
0.95 |
0.061 |
0.014 |
0.005 |
8.642 |
| Metro |
0.99 |
0.214 |
0.015 |
0.005 |
36.245 |
| DEMetro_Z |
0.0 |
0.028 |
0.016 |
0.004 |
3.272 |
| DEMetro_Z |
0.3 |
0.022 |
0.014 |
0.005 |
1.671 |
| DEMetro_Z |
0.5 |
0.028 |
0.014 |
0.003 |
5.365 |
| DEMetro_Z |
0.9 |
0.031 |
0.014 |
0.005 |
3.202 |
| DEMetro_Z |
0.95 |
0.028 |
0.014 |
0.005 |
2.497 |
| DEMetro_Z |
0.99 |
0.023 |
0.015 |
0.005 |
1.430 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
Mode Transitions
KDE + Init Plots
Forest & Ridge Plots
Pooled
Chain
Pairwise Scatter Plots
Pooled
0.0
0.3
0.5
0.9
0.95
0.99
Chain
0.0
0.3
0.5
0.9
0.95
0.99
Vary_only_Dimension
(MvNormal,
dimension,
12 runs)
Pooled Chains results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
-1.392 |
0.178 |
-0.556 |
| HMC |
5 |
-1.049 |
0.306 |
-0.435 |
| HMC |
8 |
-0.261 |
0.797 |
-0.088 |
| HMC |
12 |
-2.977 |
0.0071 |
-1.338 |
| HMC |
15 |
-0.987 |
0.336 |
-0.538 |
| HMC |
30 |
-2.710 |
0.0136 |
-0.956 |
| SMC |
2 |
-2.007 |
0.0579 |
-0.741 |
| SMC |
5 |
0.360 |
0.723 |
0.204 |
| SMC |
8 |
-0.818 |
0.425 |
-0.268 |
| SMC |
12 |
-0.607 |
0.552 |
-0.359 |
| SMC |
15 |
0.247 |
0.808 |
0.088 |
| SMC |
30 |
0.412 |
0.684 |
0.164 |
| Metro |
2 |
0.128 |
0.9 |
0.091 |
| Metro |
5 |
4.997 |
9.87e-05 |
2.872 |
| Metro |
8 |
4.003 |
0.000623 |
1.781 |
| Metro |
12 |
5.230 |
6.44e-05 |
3.090 |
| Metro |
15 |
7.236 |
1.52e-06 |
4.457 |
| Metro |
30 |
9.552 |
6.63e-09 |
4.701 |
| DEMetro_Z |
2 |
2.581 |
0.0222 |
2.283 |
| DEMetro_Z |
5 |
6.378 |
5.24e-05 |
419.458 |
| DEMetro_Z |
8 |
9.786 |
9.17e-07 |
490.906 |
| DEMetro_Z |
12 |
16.450 |
4.3e-09 |
1538.586 |
| DEMetro_Z |
15 |
19.378 |
7.5e-10 |
1641.248 |
| DEMetro_Z |
30 |
22.188 |
1.75e-10 |
1685.553 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
-3.479
|
0.00516
|
-1.004
|
| HMC_vs_DEMetro_Z |
1
|
-6.394
|
5.12e-05
|
-1.846
|
| HMC_vs_DEMetro_Z |
2
|
-9.795
|
9.09e-07
|
-2.828
|
| HMC_vs_DEMetro_Z |
3
|
-16.454
|
4.29e-09
|
-4.750
|
| HMC_vs_DEMetro_Z |
4
|
-19.348
|
7.62e-10
|
-5.585
|
| HMC_vs_DEMetro_Z |
5
|
-22.208
|
1.73e-10
|
-6.411
|
| Metro_vs_SMC |
0
|
1.213
|
0.251
|
0.350
|
| Metro_vs_SMC |
1
|
3.859
|
0.00266
|
1.114
|
| Metro_vs_SMC |
2
|
6.401
|
5.07e-05
|
1.848
|
| Metro_vs_SMC |
3
|
6.547
|
4.15e-05
|
1.890
|
| Metro_vs_SMC |
4
|
8.113
|
5.72e-06
|
2.342
|
| Metro_vs_SMC |
5
|
15.417
|
8.54e-09
|
4.450
|
| Metro_vs_DEMetro_Z |
0
|
-1.939
|
0.0786
|
-0.560
|
| Metro_vs_DEMetro_Z |
1
|
-6.339
|
5.53e-05
|
-1.830
|
| Metro_vs_DEMetro_Z |
2
|
-9.773
|
9.3e-07
|
-2.821
|
| Metro_vs_DEMetro_Z |
3
|
-16.425
|
4.37e-09
|
-4.742
|
| Metro_vs_DEMetro_Z |
4
|
-19.319
|
7.75e-10
|
-5.577
|
| Metro_vs_DEMetro_Z |
5
|
-22.140
|
1.79e-10
|
-6.391
|
| HMC_vs_Metro |
0
|
-0.963
|
0.356
|
-0.278
|
| HMC_vs_Metro |
1
|
-6.211
|
6.61e-05
|
-1.793
|
| HMC_vs_Metro |
2
|
-5.477
|
0.000193
|
-1.581
|
| HMC_vs_Metro |
3
|
-9.276
|
1.56e-06
|
-2.678
|
| HMC_vs_Metro |
4
|
-7.813
|
8.18e-06
|
-2.255
|
| HMC_vs_Metro |
5
|
-10.439
|
4.81e-07
|
-3.013
|
| HMC_vs_SMC |
0
|
0.574
|
0.577
|
0.166
|
| HMC_vs_SMC |
1
|
-1.293
|
0.223
|
-0.373
|
| HMC_vs_SMC |
2
|
0.862
|
0.407
|
0.249
|
| HMC_vs_SMC |
3
|
-2.358
|
0.0379
|
-0.681
|
| HMC_vs_SMC |
4
|
-1.342
|
0.207
|
-0.387
|
| HMC_vs_SMC |
5
|
-2.912
|
0.0141
|
-0.841
|
| DEMetro_Z_vs_SMC |
0
|
3.576
|
0.00435
|
1.032
|
| DEMetro_Z_vs_SMC |
1
|
6.384
|
5.19e-05
|
1.843
|
| DEMetro_Z_vs_SMC |
2
|
9.799
|
9.06e-07
|
2.829
|
| DEMetro_Z_vs_SMC |
3
|
16.455
|
4.28e-09
|
4.750
|
| DEMetro_Z_vs_SMC |
4
|
19.378
|
7.5e-10
|
5.594
|
| DEMetro_Z_vs_SMC |
5
|
22.206
|
1.73e-10
|
6.410
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.021 |
0.025 |
0.008 |
-0.556 |
| HMC |
5 |
0.019 |
0.022 |
0.006 |
-0.435 |
| HMC |
8 |
0.020 |
0.021 |
0.009 |
-0.088 |
| HMC |
12 |
0.019 |
0.024 |
0.004 |
-1.338 |
| HMC |
15 |
0.020 |
0.022 |
0.004 |
-0.538 |
| HMC |
30 |
0.018 |
0.021 |
0.004 |
-0.956 |
| SMC |
2 |
0.019 |
0.025 |
0.008 |
-0.741 |
| SMC |
5 |
0.023 |
0.022 |
0.006 |
0.204 |
| SMC |
8 |
0.019 |
0.021 |
0.009 |
-0.268 |
| SMC |
12 |
0.023 |
0.024 |
0.004 |
-0.359 |
| SMC |
15 |
0.022 |
0.022 |
0.004 |
0.088 |
| SMC |
30 |
0.022 |
0.021 |
0.004 |
0.164 |
| Metro |
2 |
0.026 |
0.025 |
0.008 |
0.091 |
| Metro |
5 |
0.040 |
0.022 |
0.006 |
2.872 |
| Metro |
8 |
0.038 |
0.021 |
0.009 |
1.781 |
| Metro |
12 |
0.036 |
0.024 |
0.004 |
3.090 |
| Metro |
15 |
0.038 |
0.022 |
0.004 |
4.457 |
| Metro |
30 |
0.039 |
0.021 |
0.004 |
4.701 |
| DEMetro_Z |
2 |
0.044 |
0.025 |
0.008 |
2.283 |
| DEMetro_Z |
5 |
2.669 |
0.022 |
0.006 |
419.458 |
| DEMetro_Z |
8 |
4.551 |
0.021 |
0.009 |
490.906 |
| DEMetro_Z |
12 |
5.881 |
0.024 |
0.004 |
1538.586 |
| DEMetro_Z |
15 |
5.915 |
0.022 |
0.004 |
1641.248 |
| DEMetro_Z |
30 |
6.427 |
0.021 |
0.004 |
1685.553 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
1.686 |
0.108 |
0.863 |
| HMC |
5 |
1.761 |
0.0948 |
0.962 |
| HMC |
8 |
2.129 |
0.0458 |
1.040 |
| HMC |
12 |
2.982 |
0.00927 |
2.144 |
| HMC |
15 |
3.201 |
0.00558 |
2.105 |
| HMC |
30 |
5.126 |
0.000112 |
3.520 |
| SMC |
2 |
-0.358 |
0.724 |
-0.164 |
| SMC |
5 |
1.264 |
0.223 |
0.737 |
| SMC |
8 |
0.535 |
0.598 |
0.211 |
| SMC |
12 |
0.495 |
0.625 |
0.230 |
| SMC |
15 |
0.489 |
0.629 |
0.216 |
| SMC |
30 |
3.573 |
0.00183 |
1.300 |
| Metro |
2 |
1.770 |
0.0932 |
0.956 |
| Metro |
5 |
3.087 |
0.00734 |
2.146 |
| Metro |
8 |
4.759 |
0.000172 |
2.791 |
| Metro |
12 |
8.445 |
4.24e-07 |
6.073 |
| Metro |
15 |
8.395 |
7.49e-08 |
4.358 |
| Metro |
30 |
10.586 |
1.2e-09 |
5.223 |
| DEMetro_Z |
2 |
4.644 |
0.000306 |
3.284 |
| DEMetro_Z |
5 |
3.062 |
0.0108 |
6236.104 |
| DEMetro_Z |
8 |
9.306 |
1.51e-06 |
16249.871 |
| DEMetro_Z |
12 |
14.335 |
1.83e-08 |
30547.038 |
| DEMetro_Z |
15 |
13.021 |
5e-08 |
29793.580 |
| DEMetro_Z |
30 |
22.229 |
1.72e-10 |
39854.415 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
2.029
|
0.0674
|
0.586
|
| HMC_vs_SMC |
1
|
0.338
|
0.742
|
0.098
|
| HMC_vs_SMC |
2
|
2.212
|
0.0491
|
0.639
|
| HMC_vs_SMC |
3
|
3.380
|
0.00614
|
0.976
|
| HMC_vs_SMC |
4
|
2.959
|
0.013
|
0.854
|
| HMC_vs_SMC |
5
|
2.890
|
0.0147
|
0.834
|
| Metro_vs_DEMetro_Z |
0
|
-2.832
|
0.0163
|
-0.818
|
| Metro_vs_DEMetro_Z |
1
|
-3.061
|
0.0108
|
-0.884
|
| Metro_vs_DEMetro_Z |
2
|
-9.306
|
1.51e-06
|
-2.686
|
| Metro_vs_DEMetro_Z |
3
|
-14.333
|
1.84e-08
|
-4.138
|
| Metro_vs_DEMetro_Z |
4
|
-13.019
|
5.01e-08
|
-3.758
|
| Metro_vs_DEMetro_Z |
5
|
-22.226
|
1.72e-10
|
-6.416
|
| HMC_vs_Metro |
0
|
-0.207
|
0.84
|
-0.060
|
| HMC_vs_Metro |
1
|
-2.144
|
0.0552
|
-0.619
|
| HMC_vs_Metro |
2
|
-2.923
|
0.0139
|
-0.844
|
| HMC_vs_Metro |
3
|
-5.413
|
0.000212
|
-1.563
|
| HMC_vs_Metro |
4
|
-2.620
|
0.0238
|
-0.756
|
| HMC_vs_Metro |
5
|
-1.927
|
0.0802
|
-0.556
|
| HMC_vs_DEMetro_Z |
0
|
-5.236
|
0.000279
|
-1.511
|
| HMC_vs_DEMetro_Z |
1
|
-3.061
|
0.0108
|
-0.884
|
| HMC_vs_DEMetro_Z |
2
|
-9.305
|
1.51e-06
|
-2.686
|
| HMC_vs_DEMetro_Z |
3
|
-14.334
|
1.84e-08
|
-4.138
|
| HMC_vs_DEMetro_Z |
4
|
-13.021
|
5.01e-08
|
-3.759
|
| HMC_vs_DEMetro_Z |
5
|
-22.228
|
1.72e-10
|
-6.417
|
| Metro_vs_SMC |
0
|
2.599
|
0.0247
|
0.750
|
| Metro_vs_SMC |
1
|
1.734
|
0.111
|
0.500
|
| Metro_vs_SMC |
2
|
5.108
|
0.00034
|
1.475
|
| Metro_vs_SMC |
3
|
9.971
|
7.61e-07
|
2.878
|
| Metro_vs_SMC |
4
|
8.275
|
4.73e-06
|
2.389
|
| Metro_vs_SMC |
5
|
9.437
|
1.32e-06
|
2.724
|
| DEMetro_Z_vs_SMC |
0
|
4.884
|
0.000484
|
1.410
|
| DEMetro_Z_vs_SMC |
1
|
3.062
|
0.0108
|
0.884
|
| DEMetro_Z_vs_SMC |
2
|
9.307
|
1.51e-06
|
2.687
|
| DEMetro_Z_vs_SMC |
3
|
14.335
|
1.84e-08
|
4.138
|
| DEMetro_Z_vs_SMC |
4
|
13.021
|
5e-08
|
3.759
|
| DEMetro_Z_vs_SMC |
5
|
22.228
|
1.72e-10
|
6.417
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.041 |
0.030 |
0.013 |
0.863 |
| HMC |
5 |
0.035 |
0.027 |
0.008 |
0.962 |
| HMC |
8 |
0.036 |
0.028 |
0.008 |
1.040 |
| HMC |
12 |
0.039 |
0.031 |
0.004 |
2.144 |
| HMC |
15 |
0.042 |
0.032 |
0.005 |
2.105 |
| HMC |
30 |
0.045 |
0.030 |
0.004 |
3.520 |
| SMC |
2 |
0.028 |
0.030 |
0.013 |
-0.164 |
| SMC |
5 |
0.033 |
0.027 |
0.008 |
0.737 |
| SMC |
8 |
0.029 |
0.028 |
0.008 |
0.211 |
| SMC |
12 |
0.032 |
0.031 |
0.004 |
0.230 |
| SMC |
15 |
0.033 |
0.032 |
0.005 |
0.216 |
| SMC |
30 |
0.036 |
0.030 |
0.004 |
1.300 |
| Metro |
2 |
0.043 |
0.030 |
0.013 |
0.956 |
| Metro |
5 |
0.045 |
0.027 |
0.008 |
2.146 |
| Metro |
8 |
0.049 |
0.028 |
0.008 |
2.791 |
| Metro |
12 |
0.054 |
0.031 |
0.004 |
6.073 |
| Metro |
15 |
0.053 |
0.032 |
0.005 |
4.358 |
| Metro |
30 |
0.052 |
0.030 |
0.004 |
5.223 |
| DEMetro_Z |
2 |
0.074 |
0.030 |
0.013 |
3.284 |
| DEMetro_Z |
5 |
50.722 |
0.027 |
0.008 |
6236.104 |
| DEMetro_Z |
8 |
122.836 |
0.028 |
0.008 |
16249.871 |
| DEMetro_Z |
12 |
118.279 |
0.031 |
0.004 |
30547.038 |
| DEMetro_Z |
15 |
145.270 |
0.032 |
0.005 |
29793.580 |
| DEMetro_Z |
30 |
164.523 |
0.030 |
0.004 |
39854.415 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
-0.824 |
0.419 |
-0.410 |
| HMC |
5 |
-0.182 |
0.857 |
-0.071 |
| HMC |
8 |
-0.275 |
0.787 |
-0.094 |
| HMC |
12 |
-1.457 |
0.159 |
-0.610 |
| HMC |
15 |
0.808 |
0.428 |
0.389 |
| HMC |
30 |
0.286 |
0.778 |
0.100 |
| SMC |
2 |
-1.820 |
0.0826 |
-0.797 |
| SMC |
5 |
1.085 |
0.29 |
0.486 |
| SMC |
8 |
-1.524 |
0.148 |
-0.484 |
| SMC |
12 |
-0.538 |
0.597 |
-0.285 |
| SMC |
15 |
1.085 |
0.29 |
0.398 |
| SMC |
30 |
1.042 |
0.309 |
0.435 |
| Metro |
2 |
2.115 |
0.0531 |
1.784 |
| Metro |
5 |
6.524 |
6.27e-06 |
4.142 |
| Metro |
8 |
4.836 |
9.59e-05 |
2.335 |
| Metro |
12 |
6.628 |
3.84e-06 |
3.894 |
| Metro |
15 |
7.137 |
4e-06 |
5.438 |
| Metro |
30 |
11.080 |
4.3e-09 |
6.889 |
| DEMetro_Z |
2 |
6.485 |
2.22e-05 |
6.806 |
| DEMetro_Z |
5 |
6.736 |
3.22e-05 |
1024.884 |
| DEMetro_Z |
8 |
16.066 |
5.52e-09 |
1398.626 |
| DEMetro_Z |
12 |
19.832 |
5.85e-10 |
3488.533 |
| DEMetro_Z |
15 |
25.152 |
4.52e-11 |
3926.191 |
| DEMetro_Z |
30 |
44.568 |
8.86e-14 |
5288.964 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
-4.495
|
0.000909
|
-1.298
|
| Metro_vs_DEMetro_Z |
1
|
-6.716
|
3.31e-05
|
-1.939
|
| Metro_vs_DEMetro_Z |
2
|
-16.082
|
5.46e-09
|
-4.642
|
| Metro_vs_DEMetro_Z |
3
|
-19.813
|
5.91e-10
|
-5.719
|
| Metro_vs_DEMetro_Z |
4
|
-25.086
|
4.65e-11
|
-7.242
|
| Metro_vs_DEMetro_Z |
5
|
-44.481
|
9.06e-14
|
-12.840
|
| DEMetro_Z_vs_SMC |
0
|
8.377
|
4.2e-06
|
2.418
|
| DEMetro_Z_vs_SMC |
1
|
6.735
|
3.22e-05
|
1.944
|
| DEMetro_Z_vs_SMC |
2
|
16.078
|
5.48e-09
|
4.641
|
| DEMetro_Z_vs_SMC |
3
|
19.840
|
5.82e-10
|
5.727
|
| DEMetro_Z_vs_SMC |
4
|
25.149
|
4.52e-11
|
7.260
|
| DEMetro_Z_vs_SMC |
5
|
44.556
|
8.89e-14
|
12.862
|
| HMC_vs_DEMetro_Z |
0
|
-8.112
|
5.72e-06
|
-2.342
|
| HMC_vs_DEMetro_Z |
1
|
-6.738
|
3.21e-05
|
-1.945
|
| HMC_vs_DEMetro_Z |
2
|
-16.074
|
5.49e-09
|
-4.640
|
| HMC_vs_DEMetro_Z |
3
|
-19.838
|
5.83e-10
|
-5.727
|
| HMC_vs_DEMetro_Z |
4
|
-25.165
|
4.49e-11
|
-7.264
|
| HMC_vs_DEMetro_Z |
5
|
-44.586
|
8.83e-14
|
-12.871
|
| HMC_vs_Metro |
0
|
-2.716
|
0.0201
|
-0.784
|
| HMC_vs_Metro |
1
|
-7.571
|
1.1e-05
|
-2.186
|
| HMC_vs_Metro |
2
|
-6.997
|
2.28e-05
|
-2.020
|
| HMC_vs_Metro |
3
|
-10.845
|
3.27e-07
|
-3.131
|
| HMC_vs_Metro |
4
|
-6.075
|
8.02e-05
|
-1.754
|
| HMC_vs_Metro |
5
|
-10.768
|
3.51e-07
|
-3.108
|
| HMC_vs_SMC |
0
|
0.813
|
0.433
|
0.235
|
| HMC_vs_SMC |
1
|
-1.628
|
0.132
|
-0.470
|
| HMC_vs_SMC |
2
|
1.822
|
0.0957
|
0.526
|
| HMC_vs_SMC |
3
|
-0.800
|
0.441
|
-0.231
|
| HMC_vs_SMC |
4
|
-0.020
|
0.985
|
-0.006
|
| HMC_vs_SMC |
5
|
-0.852
|
0.412
|
-0.246
|
| Metro_vs_SMC |
0
|
3.205
|
0.00837
|
0.925
|
| Metro_vs_SMC |
1
|
5.821
|
0.000116
|
1.680
|
| Metro_vs_SMC |
2
|
7.819
|
8.11e-06
|
2.257
|
| Metro_vs_SMC |
3
|
7.715
|
9.21e-06
|
2.227
|
| Metro_vs_SMC |
4
|
6.937
|
2.46e-05
|
2.003
|
| Metro_vs_SMC |
5
|
16.799
|
3.44e-09
|
4.850
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.031 |
0.032 |
0.004 |
-0.410 |
| HMC |
5 |
0.028 |
0.029 |
0.004 |
-0.071 |
| HMC |
8 |
0.029 |
0.029 |
0.005 |
-0.094 |
| HMC |
12 |
0.028 |
0.030 |
0.003 |
-0.610 |
| HMC |
15 |
0.030 |
0.029 |
0.002 |
0.389 |
| HMC |
30 |
0.028 |
0.028 |
0.002 |
0.100 |
| SMC |
2 |
0.029 |
0.032 |
0.004 |
-0.797 |
| SMC |
5 |
0.030 |
0.029 |
0.004 |
0.486 |
| SMC |
8 |
0.027 |
0.029 |
0.005 |
-0.484 |
| SMC |
12 |
0.029 |
0.030 |
0.003 |
-0.285 |
| SMC |
15 |
0.030 |
0.029 |
0.002 |
0.398 |
| SMC |
30 |
0.029 |
0.028 |
0.002 |
0.435 |
| Metro |
2 |
0.040 |
0.032 |
0.004 |
1.784 |
| Metro |
5 |
0.045 |
0.029 |
0.004 |
4.142 |
| Metro |
8 |
0.042 |
0.029 |
0.005 |
2.335 |
| Metro |
12 |
0.040 |
0.030 |
0.003 |
3.894 |
| Metro |
15 |
0.041 |
0.029 |
0.002 |
5.438 |
| Metro |
30 |
0.041 |
0.028 |
0.002 |
6.889 |
| DEMetro_Z |
2 |
0.060 |
0.032 |
0.004 |
6.806 |
| DEMetro_Z |
5 |
4.078 |
0.029 |
0.004 |
1024.884 |
| DEMetro_Z |
8 |
7.486 |
0.029 |
0.005 |
1398.626 |
| DEMetro_Z |
12 |
8.772 |
0.030 |
0.003 |
3488.533 |
| DEMetro_Z |
15 |
9.090 |
0.029 |
0.002 |
3926.191 |
| DEMetro_Z |
30 |
10.080 |
0.028 |
0.002 |
5288.964 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
-0.575 |
0.571 |
-0.264 |
| HMC |
5 |
-0.314 |
0.757 |
-0.125 |
| HMC |
8 |
0.257 |
0.8 |
0.088 |
| HMC |
12 |
-2.081 |
0.0498 |
-0.961 |
| HMC |
15 |
0.273 |
0.787 |
0.123 |
| HMC |
30 |
-0.670 |
0.511 |
-0.236 |
| SMC |
2 |
-1.657 |
0.112 |
-0.609 |
| SMC |
5 |
0.897 |
0.38 |
0.422 |
| SMC |
8 |
-0.981 |
0.341 |
-0.314 |
| SMC |
12 |
-0.683 |
0.503 |
-0.392 |
| SMC |
15 |
0.072 |
0.943 |
0.026 |
| SMC |
30 |
0.358 |
0.723 |
0.140 |
| Metro |
2 |
1.704 |
0.109 |
1.218 |
| Metro |
5 |
5.606 |
2.13e-05 |
2.966 |
| Metro |
8 |
4.418 |
0.00024 |
2.044 |
| Metro |
12 |
6.808 |
1.77e-06 |
3.621 |
| Metro |
15 |
7.441 |
8.89e-07 |
4.414 |
| Metro |
30 |
9.401 |
6.6e-09 |
4.448 |
| DEMetro_Z |
2 |
5.663 |
5.16e-05 |
4.378 |
| DEMetro_Z |
5 |
28.965 |
8.88e-12 |
166.697 |
| DEMetro_Z |
8 |
32.586 |
2.25e-12 |
138.406 |
| DEMetro_Z |
12 |
58.704 |
3.67e-15 |
303.788 |
| DEMetro_Z |
15 |
50.384 |
2.07e-14 |
307.443 |
| DEMetro_Z |
30 |
59.409 |
3.12e-15 |
282.855 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
7.447
|
1.28e-05
|
2.150
|
| DEMetro_Z_vs_SMC |
1
|
29.565
|
7.81e-12
|
8.535
|
| DEMetro_Z_vs_SMC |
2
|
32.556
|
2.74e-12
|
9.398
|
| DEMetro_Z_vs_SMC |
3
|
55.534
|
7.96e-15
|
16.031
|
| DEMetro_Z_vs_SMC |
4
|
50.416
|
2.3e-14
|
14.554
|
| DEMetro_Z_vs_SMC |
5
|
60.008
|
3.4e-15
|
17.323
|
| HMC_vs_Metro |
0
|
-2.041
|
0.066
|
-0.589
|
| HMC_vs_Metro |
1
|
-6.553
|
4.12e-05
|
-1.892
|
| HMC_vs_Metro |
2
|
-4.944
|
0.000439
|
-1.427
|
| HMC_vs_Metro |
3
|
-11.040
|
2.73e-07
|
-3.187
|
| HMC_vs_Metro |
4
|
-7.719
|
9.16e-06
|
-2.228
|
| HMC_vs_Metro |
5
|
-9.088
|
1.9e-06
|
-2.624
|
| Metro_vs_DEMetro_Z |
0
|
-4.372
|
0.00111
|
-1.262
|
| Metro_vs_DEMetro_Z |
1
|
-28.196
|
1.31e-11
|
-8.139
|
| Metro_vs_DEMetro_Z |
2
|
-30.995
|
4.68e-12
|
-8.947
|
| Metro_vs_DEMetro_Z |
3
|
-56.053
|
7.19e-15
|
-16.181
|
| Metro_vs_DEMetro_Z |
4
|
-49.632
|
2.73e-14
|
-14.328
|
| Metro_vs_DEMetro_Z |
5
|
-58.351
|
4.63e-15
|
-16.845
|
| HMC_vs_SMC |
0
|
1.192
|
0.258
|
0.344
|
| HMC_vs_SMC |
1
|
-1.744
|
0.109
|
-0.503
|
| HMC_vs_SMC |
2
|
2.136
|
0.056
|
0.617
|
| HMC_vs_SMC |
3
|
-1.367
|
0.199
|
-0.395
|
| HMC_vs_SMC |
4
|
0.309
|
0.763
|
0.089
|
| HMC_vs_SMC |
5
|
-1.067
|
0.309
|
-0.308
|
| Metro_vs_SMC |
0
|
2.538
|
0.0276
|
0.733
|
| Metro_vs_SMC |
1
|
4.678
|
0.000674
|
1.350
|
| Metro_vs_SMC |
2
|
6.734
|
3.23e-05
|
1.944
|
| Metro_vs_SMC |
3
|
7.855
|
7.77e-06
|
2.268
|
| Metro_vs_SMC |
4
|
8.813
|
2.57e-06
|
2.544
|
| Metro_vs_SMC |
5
|
13.150
|
4.52e-08
|
3.796
|
| HMC_vs_DEMetro_Z |
0
|
-7.811
|
8.2e-06
|
-2.255
|
| HMC_vs_DEMetro_Z |
1
|
-29.713
|
7.4e-12
|
-8.578
|
| HMC_vs_DEMetro_Z |
2
|
-32.990
|
2.37e-12
|
-9.524
|
| HMC_vs_DEMetro_Z |
3
|
-56.859
|
6.15e-15
|
-16.414
|
| HMC_vs_DEMetro_Z |
4
|
-49.535
|
2.79e-14
|
-14.300
|
| HMC_vs_DEMetro_Z |
5
|
-59.690
|
3.61e-15
|
-17.231
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.015 |
0.016 |
0.004 |
-0.264 |
| HMC |
5 |
0.014 |
0.014 |
0.003 |
-0.125 |
| HMC |
8 |
0.014 |
0.014 |
0.004 |
0.088 |
| HMC |
12 |
0.013 |
0.015 |
0.002 |
-0.961 |
| HMC |
15 |
0.014 |
0.014 |
0.002 |
0.123 |
| HMC |
30 |
0.013 |
0.014 |
0.002 |
-0.236 |
| SMC |
2 |
0.014 |
0.016 |
0.004 |
-0.609 |
| SMC |
5 |
0.015 |
0.014 |
0.003 |
0.422 |
| SMC |
8 |
0.013 |
0.014 |
0.004 |
-0.314 |
| SMC |
12 |
0.014 |
0.015 |
0.002 |
-0.392 |
| SMC |
15 |
0.014 |
0.014 |
0.002 |
0.026 |
| SMC |
30 |
0.014 |
0.014 |
0.002 |
0.140 |
| Metro |
2 |
0.020 |
0.016 |
0.004 |
1.218 |
| Metro |
5 |
0.024 |
0.014 |
0.003 |
2.966 |
| Metro |
8 |
0.023 |
0.014 |
0.004 |
2.044 |
| Metro |
12 |
0.022 |
0.015 |
0.002 |
3.621 |
| Metro |
15 |
0.022 |
0.014 |
0.002 |
4.414 |
| Metro |
30 |
0.023 |
0.014 |
0.002 |
4.448 |
| DEMetro_Z |
2 |
0.032 |
0.016 |
0.004 |
4.378 |
| DEMetro_Z |
5 |
0.567 |
0.014 |
0.003 |
166.697 |
| DEMetro_Z |
8 |
0.606 |
0.014 |
0.004 |
138.406 |
| DEMetro_Z |
12 |
0.579 |
0.015 |
0.002 |
303.788 |
| DEMetro_Z |
15 |
0.591 |
0.014 |
0.002 |
307.443 |
| DEMetro_Z |
30 |
0.573 |
0.014 |
0.002 |
282.855 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
R Hat (scatter)
Mode Transitions
One Chain results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
-0.665 |
0.513 |
-0.313 |
| HMC |
5 |
-0.745 |
0.464 |
-0.282 |
| HMC |
8 |
-0.177 |
0.861 |
-0.064 |
| HMC |
12 |
-1.892 |
0.0729 |
-0.912 |
| HMC |
15 |
-2.157 |
0.0426 |
-0.984 |
| HMC |
30 |
-2.223 |
0.0392 |
-0.750 |
| SMC |
2 |
-0.935 |
0.36 |
-0.424 |
| SMC |
5 |
-0.602 |
0.554 |
-0.285 |
| SMC |
8 |
0.537 |
0.597 |
0.188 |
| SMC |
12 |
-2.404 |
0.0252 |
-0.933 |
| SMC |
15 |
1.369 |
0.187 |
0.720 |
| SMC |
30 |
0.875 |
0.392 |
0.321 |
| Metro |
2 |
0.185 |
0.855 |
0.099 |
| Metro |
5 |
2.477 |
0.0231 |
1.345 |
| Metro |
8 |
4.605 |
0.00014 |
1.809 |
| Metro |
12 |
4.397 |
0.000379 |
2.594 |
| Metro |
15 |
7.107 |
1.55e-06 |
4.170 |
| Metro |
30 |
9.312 |
6.82e-09 |
4.318 |
| DEMetro_Z |
2 |
2.170 |
0.0479 |
1.823 |
| DEMetro_Z |
5 |
4.971 |
0.000422 |
201.361 |
| DEMetro_Z |
8 |
8.122 |
5.66e-06 |
598.100 |
| DEMetro_Z |
12 |
9.939 |
7.86e-07 |
2062.705 |
| DEMetro_Z |
15 |
9.800 |
9.04e-07 |
2485.359 |
| DEMetro_Z |
30 |
14.784 |
1.33e-08 |
2994.180 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
-2.255
|
0.0455
|
-0.651
|
| HMC_vs_DEMetro_Z |
1
|
-4.976
|
0.000418
|
-1.436
|
| HMC_vs_DEMetro_Z |
2
|
-8.125
|
5.64e-06
|
-2.345
|
| HMC_vs_DEMetro_Z |
3
|
-9.938
|
7.87e-07
|
-2.869
|
| HMC_vs_DEMetro_Z |
4
|
-9.806
|
8.99e-07
|
-2.831
|
| HMC_vs_DEMetro_Z |
5
|
-14.792
|
1.32e-08
|
-4.270
|
| Metro_vs_SMC |
0
|
1.255
|
0.236
|
0.362
|
| Metro_vs_SMC |
1
|
3.119
|
0.00977
|
0.900
|
| Metro_vs_SMC |
2
|
5.908
|
0.000102
|
1.706
|
| Metro_vs_SMC |
3
|
6.796
|
2.97e-05
|
1.962
|
| Metro_vs_SMC |
4
|
5.715
|
0.000135
|
1.650
|
| Metro_vs_SMC |
5
|
8.287
|
4.67e-06
|
2.392
|
| Metro_vs_DEMetro_Z |
0
|
-1.827
|
0.0949
|
-0.527
|
| Metro_vs_DEMetro_Z |
1
|
-4.924
|
0.000454
|
-1.421
|
| Metro_vs_DEMetro_Z |
2
|
-8.103
|
5.78e-06
|
-2.339
|
| Metro_vs_DEMetro_Z |
3
|
-9.928
|
7.95e-07
|
-2.866
|
| Metro_vs_DEMetro_Z |
4
|
-9.783
|
9.2e-07
|
-2.824
|
| Metro_vs_DEMetro_Z |
5
|
-14.753
|
1.36e-08
|
-4.259
|
| HMC_vs_Metro |
0
|
-0.815
|
0.432
|
-0.235
|
| HMC_vs_Metro |
1
|
-4.472
|
0.000943
|
-1.291
|
| HMC_vs_Metro |
2
|
-5.958
|
9.48e-05
|
-1.720
|
| HMC_vs_Metro |
3
|
-8.758
|
2.73e-06
|
-2.528
|
| HMC_vs_Metro |
4
|
-8.257
|
4.83e-06
|
-2.384
|
| HMC_vs_Metro |
5
|
-11.513
|
1.78e-07
|
-3.323
|
| HMC_vs_SMC |
0
|
0.299
|
0.771
|
0.086
|
| HMC_vs_SMC |
1
|
0.008
|
0.994
|
0.002
|
| HMC_vs_SMC |
2
|
-1.233
|
0.243
|
-0.356
|
| HMC_vs_SMC |
3
|
0.048
|
0.962
|
0.014
|
| HMC_vs_SMC |
4
|
-4.647
|
0.000708
|
-1.342
|
| HMC_vs_SMC |
5
|
-5.660
|
0.000147
|
-1.634
|
| DEMetro_Z_vs_SMC |
0
|
2.228
|
0.0477
|
0.643
|
| DEMetro_Z_vs_SMC |
1
|
4.998
|
0.000404
|
1.443
|
| DEMetro_Z_vs_SMC |
2
|
8.121
|
5.66e-06
|
2.344
|
| DEMetro_Z_vs_SMC |
3
|
9.939
|
7.86e-07
|
2.869
|
| DEMetro_Z_vs_SMC |
4
|
9.805
|
9e-07
|
2.830
|
| DEMetro_Z_vs_SMC |
5
|
14.780
|
1.33e-08
|
4.267
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.023 |
0.025 |
0.008 |
-0.313 |
| HMC |
5 |
0.020 |
0.022 |
0.006 |
-0.282 |
| HMC |
8 |
0.021 |
0.021 |
0.009 |
-0.064 |
| HMC |
12 |
0.020 |
0.024 |
0.004 |
-0.912 |
| HMC |
15 |
0.019 |
0.022 |
0.004 |
-0.984 |
| HMC |
30 |
0.018 |
0.021 |
0.004 |
-0.750 |
| SMC |
2 |
0.022 |
0.025 |
0.008 |
-0.424 |
| SMC |
5 |
0.020 |
0.022 |
0.006 |
-0.285 |
| SMC |
8 |
0.023 |
0.021 |
0.009 |
0.188 |
| SMC |
12 |
0.020 |
0.024 |
0.004 |
-0.933 |
| SMC |
15 |
0.025 |
0.022 |
0.004 |
0.720 |
| SMC |
30 |
0.022 |
0.021 |
0.004 |
0.321 |
| Metro |
2 |
0.026 |
0.025 |
0.008 |
0.099 |
| Metro |
5 |
0.030 |
0.022 |
0.006 |
1.345 |
| Metro |
8 |
0.038 |
0.021 |
0.009 |
1.809 |
| Metro |
12 |
0.034 |
0.024 |
0.004 |
2.594 |
| Metro |
15 |
0.037 |
0.022 |
0.004 |
4.170 |
| Metro |
30 |
0.038 |
0.021 |
0.004 |
4.318 |
| DEMetro_Z |
2 |
0.040 |
0.025 |
0.008 |
1.823 |
| DEMetro_Z |
5 |
1.292 |
0.022 |
0.006 |
201.361 |
| DEMetro_Z |
8 |
5.540 |
0.021 |
0.009 |
598.100 |
| DEMetro_Z |
12 |
7.877 |
0.024 |
0.004 |
2062.705 |
| DEMetro_Z |
15 |
8.945 |
0.022 |
0.004 |
2485.359 |
| DEMetro_Z |
30 |
11.400 |
0.021 |
0.004 |
2994.180 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
3.070 |
0.0061 |
1.542 |
| HMC |
5 |
2.114 |
0.0478 |
1.103 |
| HMC |
8 |
2.265 |
0.0354 |
1.191 |
| HMC |
12 |
3.034 |
0.00851 |
2.267 |
| HMC |
15 |
2.057 |
0.0536 |
1.075 |
| HMC |
30 |
7.618 |
2.13e-07 |
3.654 |
| SMC |
2 |
-0.147 |
0.884 |
-0.062 |
| SMC |
5 |
-0.156 |
0.877 |
-0.069 |
| SMC |
8 |
-0.451 |
0.657 |
-0.177 |
| SMC |
12 |
0.232 |
0.819 |
0.113 |
| SMC |
15 |
-1.159 |
0.26 |
-0.563 |
| SMC |
30 |
0.302 |
0.766 |
0.112 |
| Metro |
2 |
0.930 |
0.365 |
0.556 |
| Metro |
5 |
6.382 |
2.8e-06 |
3.048 |
| Metro |
8 |
5.713 |
1.9e-05 |
3.137 |
| Metro |
12 |
10.039 |
1.56e-08 |
6.113 |
| Metro |
15 |
4.471 |
0.000386 |
2.931 |
| Metro |
30 |
9.179 |
8.31e-08 |
5.946 |
| DEMetro_Z |
2 |
1.767 |
0.0966 |
1.184 |
| DEMetro_Z |
5 |
3.271 |
0.00745 |
1486.494 |
| DEMetro_Z |
8 |
5.776 |
0.000123 |
3467.223 |
| DEMetro_Z |
12 |
5.507 |
0.000184 |
6057.266 |
| DEMetro_Z |
15 |
7.754 |
8.78e-06 |
4080.764 |
| DEMetro_Z |
30 |
16.805 |
3.43e-09 |
5266.334 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
2.607
|
0.0244
|
0.753
|
| HMC_vs_SMC |
1
|
2.125
|
0.0571
|
0.613
|
| HMC_vs_SMC |
2
|
2.590
|
0.0251
|
0.748
|
| HMC_vs_SMC |
3
|
3.145
|
0.00933
|
0.908
|
| HMC_vs_SMC |
4
|
3.880
|
0.00256
|
1.120
|
| HMC_vs_SMC |
5
|
8.384
|
4.17e-06
|
2.420
|
| Metro_vs_DEMetro_Z |
0
|
-0.869
|
0.403
|
-0.251
|
| Metro_vs_DEMetro_Z |
1
|
-3.265
|
0.00754
|
-0.942
|
| Metro_vs_DEMetro_Z |
2
|
-5.771
|
0.000124
|
-1.666
|
| Metro_vs_DEMetro_Z |
3
|
-5.501
|
0.000186
|
-1.588
|
| Metro_vs_DEMetro_Z |
4
|
-7.747
|
8.85e-06
|
-2.236
|
| Metro_vs_DEMetro_Z |
5
|
-16.788
|
3.46e-09
|
-4.846
|
| HMC_vs_Metro |
0
|
1.648
|
0.128
|
0.476
|
| HMC_vs_Metro |
1
|
-3.773
|
0.00308
|
-1.089
|
| HMC_vs_Metro |
2
|
-3.113
|
0.00987
|
-0.899
|
| HMC_vs_Metro |
3
|
-4.532
|
0.000854
|
-1.308
|
| HMC_vs_Metro |
4
|
-2.938
|
0.0135
|
-0.848
|
| HMC_vs_Metro |
5
|
-3.345
|
0.00654
|
-0.966
|
| HMC_vs_DEMetro_Z |
0
|
0.415
|
0.686
|
0.120
|
| HMC_vs_DEMetro_Z |
1
|
-3.268
|
0.00749
|
-0.943
|
| HMC_vs_DEMetro_Z |
2
|
-5.774
|
0.000124
|
-1.667
|
| HMC_vs_DEMetro_Z |
3
|
-5.504
|
0.000185
|
-1.589
|
| HMC_vs_DEMetro_Z |
4
|
-7.750
|
8.82e-06
|
-2.237
|
| HMC_vs_DEMetro_Z |
5
|
-16.793
|
3.45e-09
|
-4.848
|
| Metro_vs_SMC |
0
|
0.813
|
0.433
|
0.235
|
| Metro_vs_SMC |
1
|
11.361
|
2.04e-07
|
3.280
|
| Metro_vs_SMC |
2
|
7.972
|
6.75e-06
|
2.301
|
| Metro_vs_SMC |
3
|
11.902
|
1.27e-07
|
3.436
|
| Metro_vs_SMC |
4
|
5.648
|
0.000149
|
1.630
|
| Metro_vs_SMC |
5
|
11.004
|
2.82e-07
|
3.177
|
| DEMetro_Z_vs_SMC |
0
|
2.028
|
0.0675
|
0.585
|
| DEMetro_Z_vs_SMC |
1
|
3.272
|
0.00744
|
0.945
|
| DEMetro_Z_vs_SMC |
2
|
5.778
|
0.000123
|
1.668
|
| DEMetro_Z_vs_SMC |
3
|
5.507
|
0.000184
|
1.590
|
| DEMetro_Z_vs_SMC |
4
|
7.756
|
8.76e-06
|
2.239
|
| DEMetro_Z_vs_SMC |
5
|
16.801
|
3.44e-09
|
4.850
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.050 |
0.030 |
0.013 |
1.542 |
| HMC |
5 |
0.036 |
0.027 |
0.008 |
1.103 |
| HMC |
8 |
0.037 |
0.028 |
0.008 |
1.191 |
| HMC |
12 |
0.039 |
0.031 |
0.004 |
2.267 |
| HMC |
15 |
0.037 |
0.032 |
0.005 |
1.075 |
| HMC |
30 |
0.046 |
0.030 |
0.004 |
3.654 |
| SMC |
2 |
0.029 |
0.030 |
0.013 |
-0.062 |
| SMC |
5 |
0.027 |
0.027 |
0.008 |
-0.069 |
| SMC |
8 |
0.026 |
0.028 |
0.008 |
-0.177 |
| SMC |
12 |
0.031 |
0.031 |
0.004 |
0.113 |
| SMC |
15 |
0.029 |
0.032 |
0.005 |
-0.563 |
| SMC |
30 |
0.031 |
0.030 |
0.004 |
0.112 |
| Metro |
2 |
0.037 |
0.030 |
0.013 |
0.556 |
| Metro |
5 |
0.052 |
0.027 |
0.008 |
3.048 |
| Metro |
8 |
0.051 |
0.028 |
0.008 |
3.137 |
| Metro |
12 |
0.054 |
0.031 |
0.004 |
6.113 |
| Metro |
15 |
0.046 |
0.032 |
0.005 |
2.931 |
| Metro |
30 |
0.055 |
0.030 |
0.004 |
5.946 |
| DEMetro_Z |
2 |
0.046 |
0.030 |
0.013 |
1.184 |
| DEMetro_Z |
5 |
12.111 |
0.027 |
0.008 |
1486.494 |
| DEMetro_Z |
8 |
26.231 |
0.028 |
0.008 |
3467.223 |
| DEMetro_Z |
12 |
23.478 |
0.031 |
0.004 |
6057.266 |
| DEMetro_Z |
15 |
19.925 |
0.032 |
0.005 |
4080.764 |
| DEMetro_Z |
30 |
21.766 |
0.030 |
0.004 |
5266.334 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
0.295 |
0.772 |
0.167 |
| HMC |
5 |
0.111 |
0.912 |
0.043 |
| HMC |
8 |
-0.101 |
0.921 |
-0.039 |
| HMC |
12 |
0.066 |
0.948 |
0.028 |
| HMC |
15 |
-0.490 |
0.629 |
-0.177 |
| HMC |
30 |
0.483 |
0.635 |
0.166 |
| SMC |
2 |
-1.196 |
0.248 |
-0.704 |
| SMC |
5 |
-0.669 |
0.511 |
-0.329 |
| SMC |
8 |
-0.135 |
0.894 |
-0.050 |
| SMC |
12 |
-1.884 |
0.0732 |
-0.715 |
| SMC |
15 |
1.058 |
0.303 |
0.536 |
| SMC |
30 |
1.202 |
0.242 |
0.458 |
| Metro |
2 |
1.818 |
0.0864 |
1.064 |
| Metro |
5 |
3.904 |
0.00125 |
2.542 |
| Metro |
8 |
4.942 |
6.59e-05 |
2.225 |
| Metro |
12 |
5.445 |
4.37e-05 |
3.287 |
| Metro |
15 |
7.722 |
5.79e-07 |
4.643 |
| Metro |
30 |
10.662 |
6.86e-09 |
6.544 |
| DEMetro_Z |
2 |
4.858 |
0.000271 |
4.232 |
| DEMetro_Z |
5 |
5.038 |
0.000379 |
292.306 |
| DEMetro_Z |
8 |
9.111 |
1.86e-06 |
921.418 |
| DEMetro_Z |
12 |
11.081 |
2.63e-07 |
2730.990 |
| DEMetro_Z |
15 |
10.176 |
6.21e-07 |
3333.560 |
| DEMetro_Z |
30 |
14.804 |
1.31e-08 |
4929.553 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
-3.061
|
0.0108
|
-0.884
|
| Metro_vs_DEMetro_Z |
1
|
-4.989
|
0.00041
|
-1.440
|
| Metro_vs_DEMetro_Z |
2
|
-9.094
|
1.89e-06
|
-2.625
|
| Metro_vs_DEMetro_Z |
3
|
-11.071
|
2.65e-07
|
-3.196
|
| Metro_vs_DEMetro_Z |
4
|
-10.161
|
6.3e-07
|
-2.933
|
| Metro_vs_DEMetro_Z |
5
|
-14.775
|
1.34e-08
|
-4.265
|
| DEMetro_Z_vs_SMC |
0
|
4.358
|
0.00114
|
1.258
|
| DEMetro_Z_vs_SMC |
1
|
5.064
|
0.000364
|
1.462
|
| DEMetro_Z_vs_SMC |
2
|
9.116
|
1.85e-06
|
2.632
|
| DEMetro_Z_vs_SMC |
3
|
11.080
|
2.63e-07
|
3.199
|
| DEMetro_Z_vs_SMC |
4
|
10.180
|
6.19e-07
|
2.939
|
| DEMetro_Z_vs_SMC |
5
|
14.799
|
1.31e-08
|
4.272
|
| HMC_vs_DEMetro_Z |
0
|
-3.690
|
0.00356
|
-1.065
|
| HMC_vs_DEMetro_Z |
1
|
-5.031
|
0.000383
|
-1.452
|
| HMC_vs_DEMetro_Z |
2
|
-9.115
|
1.85e-06
|
-2.631
|
| HMC_vs_DEMetro_Z |
3
|
-11.074
|
2.64e-07
|
-3.197
|
| HMC_vs_DEMetro_Z |
4
|
-10.178
|
6.2e-07
|
-2.938
|
| HMC_vs_DEMetro_Z |
5
|
-14.806
|
1.31e-08
|
-4.274
|
| HMC_vs_Metro |
0
|
-1.387
|
0.193
|
-0.400
|
| HMC_vs_Metro |
1
|
-5.055
|
0.000369
|
-1.459
|
| HMC_vs_Metro |
2
|
-5.286
|
0.000258
|
-1.526
|
| HMC_vs_Metro |
3
|
-6.475
|
4.58e-05
|
-1.869
|
| HMC_vs_Metro |
4
|
-8.307
|
4.56e-06
|
-2.398
|
| HMC_vs_Metro |
5
|
-10.400
|
4.99e-07
|
-3.002
|
| HMC_vs_SMC |
0
|
2.961
|
0.0129
|
0.855
|
| HMC_vs_SMC |
1
|
0.880
|
0.398
|
0.254
|
| HMC_vs_SMC |
2
|
0.039
|
0.97
|
0.011
|
| HMC_vs_SMC |
3
|
2.318
|
0.0407
|
0.669
|
| HMC_vs_SMC |
4
|
-1.934
|
0.0793
|
-0.558
|
| HMC_vs_SMC |
5
|
-1.118
|
0.287
|
-0.323
|
| Metro_vs_SMC |
0
|
3.061
|
0.0108
|
0.884
|
| Metro_vs_SMC |
1
|
5.261
|
0.000268
|
1.519
|
| Metro_vs_SMC |
2
|
6.336
|
5.55e-05
|
1.829
|
| Metro_vs_SMC |
3
|
7.399
|
1.36e-05
|
2.136
|
| Metro_vs_SMC |
4
|
6.327
|
5.62e-05
|
1.826
|
| Metro_vs_SMC |
5
|
9.379
|
1.4e-06
|
2.707
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.033 |
0.032 |
0.004 |
0.167 |
| HMC |
5 |
0.029 |
0.029 |
0.004 |
0.043 |
| HMC |
8 |
0.029 |
0.029 |
0.005 |
-0.039 |
| HMC |
12 |
0.030 |
0.030 |
0.003 |
0.028 |
| HMC |
15 |
0.028 |
0.029 |
0.002 |
-0.177 |
| HMC |
30 |
0.029 |
0.028 |
0.002 |
0.166 |
| SMC |
2 |
0.029 |
0.032 |
0.004 |
-0.704 |
| SMC |
5 |
0.027 |
0.029 |
0.004 |
-0.329 |
| SMC |
8 |
0.029 |
0.029 |
0.005 |
-0.050 |
| SMC |
12 |
0.028 |
0.030 |
0.003 |
-0.715 |
| SMC |
15 |
0.030 |
0.029 |
0.002 |
0.536 |
| SMC |
30 |
0.029 |
0.028 |
0.002 |
0.458 |
| Metro |
2 |
0.037 |
0.032 |
0.004 |
1.064 |
| Metro |
5 |
0.039 |
0.029 |
0.004 |
2.542 |
| Metro |
8 |
0.041 |
0.029 |
0.005 |
2.225 |
| Metro |
12 |
0.038 |
0.030 |
0.003 |
3.287 |
| Metro |
15 |
0.039 |
0.029 |
0.002 |
4.643 |
| Metro |
30 |
0.041 |
0.028 |
0.002 |
6.544 |
| DEMetro_Z |
2 |
0.050 |
0.032 |
0.004 |
4.232 |
| DEMetro_Z |
5 |
1.183 |
0.029 |
0.004 |
292.306 |
| DEMetro_Z |
8 |
4.942 |
0.029 |
0.005 |
921.418 |
| DEMetro_Z |
12 |
6.874 |
0.030 |
0.003 |
2730.990 |
| DEMetro_Z |
15 |
7.723 |
0.029 |
0.002 |
3333.560 |
| DEMetro_Z |
30 |
9.397 |
0.028 |
0.002 |
4929.553 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
0.515 |
0.612 |
0.212 |
| HMC |
5 |
0.436 |
0.667 |
0.157 |
| HMC |
8 |
0.059 |
0.953 |
0.022 |
| HMC |
12 |
-1.076 |
0.294 |
-0.492 |
| HMC |
15 |
-0.881 |
0.388 |
-0.374 |
| HMC |
30 |
-0.604 |
0.554 |
-0.199 |
| SMC |
2 |
-1.491 |
0.151 |
-0.678 |
| SMC |
5 |
-0.635 |
0.532 |
-0.279 |
| SMC |
8 |
0.342 |
0.736 |
0.124 |
| SMC |
12 |
-3.019 |
0.00663 |
-1.097 |
| SMC |
15 |
1.457 |
0.162 |
0.789 |
| SMC |
30 |
0.389 |
0.701 |
0.134 |
| Metro |
2 |
0.954 |
0.352 |
0.488 |
| Metro |
5 |
3.731 |
0.00135 |
1.881 |
| Metro |
8 |
4.877 |
7.2e-05 |
1.922 |
| Metro |
12 |
5.296 |
5.14e-05 |
3.026 |
| Metro |
15 |
7.790 |
3.49e-07 |
4.355 |
| Metro |
30 |
9.623 |
3.25e-09 |
4.329 |
| DEMetro_Z |
2 |
3.162 |
0.00674 |
2.483 |
| DEMetro_Z |
5 |
10.560 |
4.11e-07 |
63.751 |
| DEMetro_Z |
8 |
28.577 |
1.04e-11 |
176.731 |
| DEMetro_Z |
12 |
47.858 |
3.9e-14 |
476.435 |
| DEMetro_Z |
15 |
74.633 |
2.74e-16 |
466.440 |
| DEMetro_Z |
30 |
93.607 |
2.06e-17 |
454.497 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
3.297
|
0.00712
|
0.952
|
| DEMetro_Z_vs_SMC |
1
|
10.719
|
3.68e-07
|
3.094
|
| DEMetro_Z_vs_SMC |
2
|
28.745
|
1.06e-11
|
8.298
|
| DEMetro_Z_vs_SMC |
3
|
47.650
|
4.26e-14
|
13.755
|
| DEMetro_Z_vs_SMC |
4
|
77.175
|
2.15e-16
|
22.278
|
| DEMetro_Z_vs_SMC |
5
|
94.925
|
2.21e-17
|
27.402
|
| HMC_vs_Metro |
0
|
-0.601
|
0.56
|
-0.174
|
| HMC_vs_Metro |
1
|
-4.801
|
0.000553
|
-1.386
|
| HMC_vs_Metro |
2
|
-5.276
|
0.000262
|
-1.523
|
| HMC_vs_Metro |
3
|
-8.831
|
2.52e-06
|
-2.549
|
| HMC_vs_Metro |
4
|
-8.249
|
4.88e-06
|
-2.381
|
| HMC_vs_Metro |
5
|
-12.798
|
5.98e-08
|
-3.695
|
| Metro_vs_DEMetro_Z |
0
|
-2.098
|
0.0598
|
-0.606
|
| Metro_vs_DEMetro_Z |
1
|
-10.562
|
4.27e-07
|
-3.049
|
| Metro_vs_DEMetro_Z |
2
|
-28.323
|
1.25e-11
|
-8.176
|
| Metro_vs_DEMetro_Z |
3
|
-48.072
|
3.87e-14
|
-13.877
|
| Metro_vs_DEMetro_Z |
4
|
-74.310
|
3.26e-16
|
-21.452
|
| Metro_vs_DEMetro_Z |
5
|
-89.001
|
4.49e-17
|
-25.692
|
| HMC_vs_SMC |
0
|
4.266
|
0.00133
|
1.232
|
| HMC_vs_SMC |
1
|
1.495
|
0.163
|
0.432
|
| HMC_vs_SMC |
2
|
-0.441
|
0.668
|
-0.127
|
| HMC_vs_SMC |
3
|
1.642
|
0.129
|
0.474
|
| HMC_vs_SMC |
4
|
-3.655
|
0.00379
|
-1.055
|
| HMC_vs_SMC |
5
|
-1.598
|
0.138
|
-0.461
|
| Metro_vs_SMC |
0
|
2.616
|
0.024
|
0.755
|
| Metro_vs_SMC |
1
|
5.427
|
0.000208
|
1.567
|
| Metro_vs_SMC |
2
|
7.442
|
1.29e-05
|
2.148
|
| Metro_vs_SMC |
3
|
8.348
|
4.35e-06
|
2.410
|
| Metro_vs_SMC |
4
|
5.645
|
0.00015
|
1.630
|
| Metro_vs_SMC |
5
|
9.632
|
1.07e-06
|
2.781
|
| HMC_vs_DEMetro_Z |
0
|
-2.522
|
0.0284
|
-0.728
|
| HMC_vs_DEMetro_Z |
1
|
-10.584
|
4.18e-07
|
-3.055
|
| HMC_vs_DEMetro_Z |
2
|
-28.419
|
1.2e-11
|
-8.204
|
| HMC_vs_DEMetro_Z |
3
|
-47.366
|
4.55e-14
|
-13.673
|
| HMC_vs_DEMetro_Z |
4
|
-75.776
|
2.63e-16
|
-21.875
|
| HMC_vs_DEMetro_Z |
5
|
-92.681
|
2.88e-17
|
-26.755
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.017 |
0.016 |
0.004 |
0.212 |
| HMC |
5 |
0.014 |
0.014 |
0.003 |
0.157 |
| HMC |
8 |
0.014 |
0.014 |
0.004 |
0.022 |
| HMC |
12 |
0.014 |
0.015 |
0.002 |
-0.492 |
| HMC |
15 |
0.013 |
0.014 |
0.002 |
-0.374 |
| HMC |
30 |
0.013 |
0.014 |
0.002 |
-0.199 |
| SMC |
2 |
0.014 |
0.016 |
0.004 |
-0.678 |
| SMC |
5 |
0.013 |
0.014 |
0.003 |
-0.279 |
| SMC |
8 |
0.014 |
0.014 |
0.004 |
0.124 |
| SMC |
12 |
0.013 |
0.015 |
0.002 |
-1.097 |
| SMC |
15 |
0.016 |
0.014 |
0.002 |
0.789 |
| SMC |
30 |
0.014 |
0.014 |
0.002 |
0.134 |
| Metro |
2 |
0.018 |
0.016 |
0.004 |
0.488 |
| Metro |
5 |
0.020 |
0.014 |
0.003 |
1.881 |
| Metro |
8 |
0.022 |
0.014 |
0.004 |
1.922 |
| Metro |
12 |
0.021 |
0.015 |
0.002 |
3.026 |
| Metro |
15 |
0.022 |
0.014 |
0.002 |
4.355 |
| Metro |
30 |
0.022 |
0.014 |
0.002 |
4.329 |
| DEMetro_Z |
2 |
0.025 |
0.016 |
0.004 |
2.483 |
| DEMetro_Z |
5 |
0.226 |
0.014 |
0.003 |
63.751 |
| DEMetro_Z |
8 |
0.770 |
0.014 |
0.004 |
176.731 |
| DEMetro_Z |
12 |
0.899 |
0.015 |
0.002 |
476.435 |
| DEMetro_Z |
15 |
0.890 |
0.014 |
0.002 |
466.440 |
| DEMetro_Z |
30 |
0.912 |
0.014 |
0.002 |
454.497 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
Mode Transitions
KDE + Init Plots
Forest & Ridge Plots
Pooled
Chain
Pairwise Scatter Plots
Pooled
Chain
Varying_only_Tails
(MvStudentT,
nu,
12 runs)
Pooled Chains results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
-0.268 |
0.792 |
-0.096 |
| HMC |
2.5 |
-0.402 |
0.692 |
-0.179 |
| HMC |
3.0 |
-0.329 |
0.746 |
-0.168 |
| HMC |
4.0 |
1.315 |
0.202 |
0.509 |
| HMC |
10.0 |
-1.650 |
0.115 |
-0.575 |
| HMC |
50.0 |
0.754 |
0.459 |
0.333 |
| SMC |
2.1 |
-0.887 |
0.387 |
-0.296 |
| SMC |
2.5 |
0.478 |
0.637 |
0.189 |
| SMC |
3.0 |
-1.204 |
0.242 |
-0.512 |
| SMC |
4.0 |
-0.211 |
0.834 |
-0.084 |
| SMC |
10.0 |
-2.276 |
0.0367 |
-0.737 |
| SMC |
50.0 |
-0.244 |
0.81 |
-0.084 |
| Metro |
2.1 |
1.791 |
0.0896 |
0.963 |
| Metro |
2.5 |
1.422 |
0.183 |
11.101 |
| Metro |
3.0 |
1.795 |
0.0982 |
2.709 |
| Metro |
4.0 |
3.474 |
0.00345 |
2.568 |
| Metro |
10.0 |
0.992 |
0.333 |
0.463 |
| Metro |
50.0 |
3.256 |
0.00554 |
2.521 |
| DEMetro_Z |
2.1 |
1.218 |
0.236 |
0.459 |
| DEMetro_Z |
2.5 |
2.980 |
0.0112 |
3.602 |
| DEMetro_Z |
3.0 |
2.664 |
0.0183 |
2.134 |
| DEMetro_Z |
4.0 |
3.129 |
0.00765 |
2.783 |
| DEMetro_Z |
10.0 |
1.510 |
0.146 |
0.554 |
| DEMetro_Z |
50.0 |
3.558 |
0.00236 |
2.098 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
-1.793
|
0.1
|
-0.518
|
| HMC_vs_DEMetro_Z |
1
|
-2.879
|
0.015
|
-0.831
|
| HMC_vs_DEMetro_Z |
2
|
-2.536
|
0.0277
|
-0.732
|
| HMC_vs_DEMetro_Z |
3
|
-2.288
|
0.0429
|
-0.661
|
| HMC_vs_DEMetro_Z |
4
|
-3.804
|
0.00292
|
-1.098
|
| HMC_vs_DEMetro_Z |
5
|
-2.650
|
0.0226
|
-0.765
|
| Metro_vs_SMC |
0
|
2.807
|
0.0171
|
0.810
|
| Metro_vs_SMC |
1
|
1.389
|
0.192
|
0.401
|
| Metro_vs_SMC |
2
|
2.273
|
0.0441
|
0.656
|
| Metro_vs_SMC |
3
|
3.169
|
0.00893
|
0.915
|
| Metro_vs_SMC |
4
|
3.315
|
0.00689
|
0.957
|
| Metro_vs_SMC |
5
|
3.659
|
0.00376
|
1.056
|
| Metro_vs_DEMetro_Z |
0
|
1.000
|
0.339
|
0.289
|
| Metro_vs_DEMetro_Z |
1
|
0.915
|
0.38
|
0.264
|
| Metro_vs_DEMetro_Z |
2
|
0.307
|
0.765
|
0.088
|
| Metro_vs_DEMetro_Z |
3
|
-0.217
|
0.832
|
-0.063
|
| Metro_vs_DEMetro_Z |
4
|
-0.210
|
0.837
|
-0.061
|
| Metro_vs_DEMetro_Z |
5
|
0.474
|
0.645
|
0.137
|
| HMC_vs_Metro |
0
|
-2.447
|
0.0324
|
-0.706
|
| HMC_vs_Metro |
1
|
-1.427
|
0.181
|
-0.412
|
| HMC_vs_Metro |
2
|
-2.077
|
0.062
|
-0.600
|
| HMC_vs_Metro |
3
|
-3.249
|
0.00774
|
-0.938
|
| HMC_vs_Metro |
4
|
-2.419
|
0.0341
|
-0.698
|
| HMC_vs_Metro |
5
|
-2.421
|
0.034
|
-0.699
|
| HMC_vs_SMC |
0
|
1.259
|
0.234
|
0.363
|
| HMC_vs_SMC |
1
|
-0.772
|
0.456
|
-0.223
|
| HMC_vs_SMC |
2
|
0.975
|
0.35
|
0.282
|
| HMC_vs_SMC |
3
|
1.417
|
0.184
|
0.409
|
| HMC_vs_SMC |
4
|
0.720
|
0.487
|
0.208
|
| HMC_vs_SMC |
5
|
0.993
|
0.342
|
0.287
|
| DEMetro_Z_vs_SMC |
0
|
4.078
|
0.00183
|
1.177
|
| DEMetro_Z_vs_SMC |
1
|
3.165
|
0.00899
|
0.914
|
| DEMetro_Z_vs_SMC |
2
|
3.141
|
0.0094
|
0.907
|
| DEMetro_Z_vs_SMC |
3
|
3.227
|
0.00807
|
0.931
|
| DEMetro_Z_vs_SMC |
4
|
5.298
|
0.000253
|
1.529
|
| DEMetro_Z_vs_SMC |
5
|
4.233
|
0.00141
|
1.222
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.068 |
0.072 |
0.040 |
-0.096 |
| HMC |
2.5 |
0.037 |
0.040 |
0.019 |
-0.179 |
| HMC |
3.0 |
0.042 |
0.045 |
0.018 |
-0.168 |
| HMC |
4.0 |
0.031 |
0.025 |
0.013 |
0.509 |
| HMC |
10.0 |
0.019 |
0.029 |
0.016 |
-0.575 |
| HMC |
50.0 |
0.019 |
0.016 |
0.010 |
0.333 |
| SMC |
2.1 |
0.060 |
0.072 |
0.040 |
-0.296 |
| SMC |
2.5 |
0.044 |
0.040 |
0.019 |
0.189 |
| SMC |
3.0 |
0.036 |
0.045 |
0.018 |
-0.512 |
| SMC |
4.0 |
0.024 |
0.025 |
0.013 |
-0.084 |
| SMC |
10.0 |
0.017 |
0.029 |
0.016 |
-0.737 |
| SMC |
50.0 |
0.015 |
0.016 |
0.010 |
-0.084 |
| Metro |
2.1 |
0.110 |
0.072 |
0.040 |
0.963 |
| Metro |
2.5 |
0.252 |
0.040 |
0.019 |
11.101 |
| Metro |
3.0 |
0.093 |
0.045 |
0.018 |
2.709 |
| Metro |
4.0 |
0.057 |
0.025 |
0.013 |
2.568 |
| Metro |
10.0 |
0.036 |
0.029 |
0.016 |
0.463 |
| Metro |
50.0 |
0.041 |
0.016 |
0.010 |
2.521 |
| DEMetro_Z |
2.1 |
0.090 |
0.072 |
0.040 |
0.459 |
| DEMetro_Z |
2.5 |
0.109 |
0.040 |
0.019 |
3.602 |
| DEMetro_Z |
3.0 |
0.083 |
0.045 |
0.018 |
2.134 |
| DEMetro_Z |
4.0 |
0.059 |
0.025 |
0.013 |
2.783 |
| DEMetro_Z |
10.0 |
0.037 |
0.029 |
0.016 |
0.554 |
| DEMetro_Z |
50.0 |
0.036 |
0.016 |
0.010 |
2.098 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
-0.012 |
0.991 |
-0.005 |
| HMC |
2.5 |
-1.040 |
0.314 |
-0.336 |
| HMC |
3.0 |
0.843 |
0.415 |
0.981 |
| HMC |
4.0 |
2.498 |
0.0241 |
1.702 |
| HMC |
10.0 |
1.695 |
0.106 |
0.881 |
| HMC |
50.0 |
1.507 |
0.146 |
0.664 |
| SMC |
2.1 |
0.096 |
0.924 |
0.037 |
| SMC |
2.5 |
0.333 |
0.745 |
0.334 |
| SMC |
3.0 |
0.249 |
0.806 |
0.098 |
| SMC |
4.0 |
1.430 |
0.169 |
0.737 |
| SMC |
10.0 |
1.999 |
0.0603 |
1.072 |
| SMC |
50.0 |
1.986 |
0.0608 |
0.970 |
| Metro |
2.1 |
-0.158 |
0.876 |
-0.062 |
| Metro |
2.5 |
0.994 |
0.341 |
7.978 |
| Metro |
3.0 |
0.957 |
0.354 |
0.739 |
| Metro |
4.0 |
3.096 |
0.00902 |
3.780 |
| Metro |
10.0 |
7.110 |
3.26e-06 |
5.022 |
| Metro |
50.0 |
2.491 |
0.0221 |
1.301 |
| DEMetro_Z |
2.1 |
0.042 |
0.967 |
0.016 |
| DEMetro_Z |
2.5 |
0.232 |
0.819 |
0.079 |
| DEMetro_Z |
3.0 |
0.341 |
0.737 |
0.128 |
| DEMetro_Z |
4.0 |
3.630 |
0.00245 |
2.614 |
| DEMetro_Z |
10.0 |
3.235 |
0.00586 |
2.571 |
| DEMetro_Z |
50.0 |
2.250 |
0.0391 |
1.509 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
-0.372
|
0.717
|
-0.107
|
| HMC_vs_SMC |
1
|
-0.676
|
0.513
|
-0.195
|
| HMC_vs_SMC |
2
|
0.911
|
0.382
|
0.263
|
| HMC_vs_SMC |
3
|
1.575
|
0.144
|
0.455
|
| HMC_vs_SMC |
4
|
-0.251
|
0.806
|
-0.073
|
| HMC_vs_SMC |
5
|
-0.671
|
0.516
|
-0.194
|
| Metro_vs_DEMetro_Z |
0
|
-2.924
|
0.0138
|
-0.844
|
| Metro_vs_DEMetro_Z |
1
|
0.977
|
0.349
|
0.282
|
| Metro_vs_DEMetro_Z |
2
|
0.826
|
0.427
|
0.238
|
| Metro_vs_DEMetro_Z |
3
|
0.768
|
0.459
|
0.222
|
| Metro_vs_DEMetro_Z |
4
|
2.454
|
0.032
|
0.708
|
| Metro_vs_DEMetro_Z |
5
|
-0.353
|
0.731
|
-0.102
|
| HMC_vs_Metro |
0
|
0.821
|
0.429
|
0.237
|
| HMC_vs_Metro |
1
|
-1.032
|
0.324
|
-0.298
|
| HMC_vs_Metro |
2
|
0.555
|
0.59
|
0.160
|
| HMC_vs_Metro |
3
|
-1.677
|
0.122
|
-0.484
|
| HMC_vs_Metro |
4
|
-4.596
|
0.000769
|
-1.327
|
| HMC_vs_Metro |
5
|
-1.119
|
0.287
|
-0.323
|
| HMC_vs_DEMetro_Z |
0
|
-0.312
|
0.761
|
-0.090
|
| HMC_vs_DEMetro_Z |
1
|
-2.542
|
0.0274
|
-0.734
|
| HMC_vs_DEMetro_Z |
2
|
0.739
|
0.475
|
0.213
|
| HMC_vs_DEMetro_Z |
3
|
-0.940
|
0.368
|
-0.271
|
| HMC_vs_DEMetro_Z |
4
|
-1.997
|
0.0711
|
-0.577
|
| HMC_vs_DEMetro_Z |
5
|
-1.038
|
0.322
|
-0.300
|
| Metro_vs_SMC |
0
|
-1.286
|
0.225
|
-0.371
|
| Metro_vs_SMC |
1
|
0.935
|
0.37
|
0.270
|
| Metro_vs_SMC |
2
|
1.157
|
0.272
|
0.334
|
| Metro_vs_SMC |
3
|
2.487
|
0.0302
|
0.718
|
| Metro_vs_SMC |
4
|
5.556
|
0.000171
|
1.604
|
| Metro_vs_SMC |
5
|
0.669
|
0.517
|
0.193
|
| DEMetro_Z_vs_SMC |
0
|
-0.261
|
0.799
|
-0.075
|
| DEMetro_Z_vs_SMC |
1
|
-0.273
|
0.79
|
-0.079
|
| DEMetro_Z_vs_SMC |
2
|
0.136
|
0.894
|
0.039
|
| DEMetro_Z_vs_SMC |
3
|
3.442
|
0.0055
|
0.994
|
| DEMetro_Z_vs_SMC |
4
|
1.472
|
0.169
|
0.425
|
| DEMetro_Z_vs_SMC |
5
|
0.797
|
0.442
|
0.230
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
8.711 |
8.779 |
15.112 |
-0.005 |
| HMC |
2.5 |
1.088 |
1.437 |
1.038 |
-0.336 |
| HMC |
3.0 |
1.638 |
0.730 |
0.925 |
0.981 |
| HMC |
4.0 |
0.226 |
0.121 |
0.062 |
1.702 |
| HMC |
10.0 |
0.048 |
0.034 |
0.016 |
0.881 |
| HMC |
50.0 |
0.037 |
0.028 |
0.015 |
0.664 |
| SMC |
2.1 |
9.337 |
8.779 |
15.112 |
0.037 |
| SMC |
2.5 |
1.784 |
1.437 |
1.038 |
0.334 |
| SMC |
3.0 |
0.821 |
0.730 |
0.925 |
0.098 |
| SMC |
4.0 |
0.166 |
0.121 |
0.062 |
0.737 |
| SMC |
10.0 |
0.051 |
0.034 |
0.016 |
1.072 |
| SMC |
50.0 |
0.042 |
0.028 |
0.015 |
0.970 |
| Metro |
2.1 |
7.849 |
8.779 |
15.112 |
-0.062 |
| Metro |
2.5 |
9.719 |
1.437 |
1.038 |
7.978 |
| Metro |
3.0 |
1.414 |
0.730 |
0.925 |
0.739 |
| Metro |
4.0 |
0.354 |
0.121 |
0.062 |
3.780 |
| Metro |
10.0 |
0.113 |
0.034 |
0.016 |
5.022 |
| Metro |
50.0 |
0.047 |
0.028 |
0.015 |
1.301 |
| DEMetro_Z |
2.1 |
9.025 |
8.779 |
15.112 |
0.016 |
| DEMetro_Z |
2.5 |
1.519 |
1.437 |
1.038 |
0.079 |
| DEMetro_Z |
3.0 |
0.849 |
0.730 |
0.925 |
0.128 |
| DEMetro_Z |
4.0 |
0.282 |
0.121 |
0.062 |
2.614 |
| DEMetro_Z |
10.0 |
0.074 |
0.034 |
0.016 |
2.571 |
| DEMetro_Z |
50.0 |
0.050 |
0.028 |
0.015 |
1.509 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
1.219 |
0.241 |
0.841 |
| HMC |
2.5 |
0.515 |
0.612 |
0.223 |
| HMC |
3.0 |
1.791 |
0.0966 |
1.781 |
| HMC |
4.0 |
3.586 |
0.00247 |
2.347 |
| HMC |
10.0 |
-0.595 |
0.56 |
-0.190 |
| HMC |
50.0 |
0.675 |
0.508 |
0.360 |
| SMC |
2.1 |
0.025 |
0.981 |
0.011 |
| SMC |
2.5 |
-0.567 |
0.577 |
-0.297 |
| SMC |
3.0 |
-0.491 |
0.629 |
-0.210 |
| SMC |
4.0 |
0.281 |
0.782 |
0.131 |
| SMC |
10.0 |
-1.699 |
0.109 |
-0.547 |
| SMC |
50.0 |
-0.065 |
0.949 |
-0.028 |
| Metro |
2.1 |
4.598 |
0.000161 |
2.165 |
| Metro |
2.5 |
1.463 |
0.171 |
16.383 |
| Metro |
3.0 |
3.186 |
0.00823 |
6.221 |
| Metro |
4.0 |
6.526 |
2.59e-05 |
8.188 |
| Metro |
10.0 |
4.240 |
0.000367 |
1.960 |
| Metro |
50.0 |
3.886 |
0.00177 |
3.541 |
| DEMetro_Z |
2.1 |
6.371 |
7.05e-06 |
3.856 |
| DEMetro_Z |
2.5 |
4.626 |
0.000585 |
6.411 |
| DEMetro_Z |
3.0 |
9.080 |
7.45e-08 |
5.634 |
| DEMetro_Z |
4.0 |
8.220 |
1.69e-06 |
8.247 |
| DEMetro_Z |
10.0 |
5.033 |
5.51e-05 |
1.865 |
| DEMetro_Z |
50.0 |
6.294 |
7.02e-06 |
3.654 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
-2.980
|
0.0125
|
-0.860
|
| Metro_vs_DEMetro_Z |
1
|
0.846
|
0.415
|
0.244
|
| Metro_vs_DEMetro_Z |
2
|
0.285
|
0.781
|
0.082
|
| Metro_vs_DEMetro_Z |
3
|
-0.033
|
0.974
|
-0.009
|
| Metro_vs_DEMetro_Z |
4
|
0.225
|
0.826
|
0.065
|
| Metro_vs_DEMetro_Z |
5
|
-0.119
|
0.907
|
-0.034
|
| DEMetro_Z_vs_SMC |
0
|
10.438
|
4.81e-07
|
3.013
|
| DEMetro_Z_vs_SMC |
1
|
5.444
|
0.000203
|
1.572
|
| DEMetro_Z_vs_SMC |
2
|
9.213
|
1.67e-06
|
2.659
|
| DEMetro_Z_vs_SMC |
3
|
7.804
|
8.26e-06
|
2.253
|
| DEMetro_Z_vs_SMC |
4
|
11.701
|
1.51e-07
|
3.378
|
| DEMetro_Z_vs_SMC |
5
|
5.797
|
0.00012
|
1.674
|
| HMC_vs_DEMetro_Z |
0
|
-3.960
|
0.00224
|
-1.143
|
| HMC_vs_DEMetro_Z |
1
|
-4.786
|
0.000566
|
-1.382
|
| HMC_vs_DEMetro_Z |
2
|
-3.454
|
0.00539
|
-0.997
|
| HMC_vs_DEMetro_Z |
3
|
-4.650
|
0.000705
|
-1.342
|
| HMC_vs_DEMetro_Z |
4
|
-8.802
|
2.6e-06
|
-2.541
|
| HMC_vs_DEMetro_Z |
5
|
-4.125
|
0.00169
|
-1.191
|
| HMC_vs_Metro |
0
|
-1.652
|
0.127
|
-0.477
|
| HMC_vs_Metro |
1
|
-1.428
|
0.181
|
-0.412
|
| HMC_vs_Metro |
2
|
-3.537
|
0.00466
|
-1.021
|
| HMC_vs_Metro |
3
|
-4.598
|
0.000768
|
-1.327
|
| HMC_vs_Metro |
4
|
-6.021
|
8.66e-05
|
-1.738
|
| HMC_vs_Metro |
5
|
-2.910
|
0.0142
|
-0.840
|
| HMC_vs_SMC |
0
|
1.065
|
0.31
|
0.307
|
| HMC_vs_SMC |
1
|
0.915
|
0.38
|
0.264
|
| HMC_vs_SMC |
2
|
2.391
|
0.0358
|
0.690
|
| HMC_vs_SMC |
3
|
2.938
|
0.0135
|
0.848
|
| HMC_vs_SMC |
4
|
2.633
|
0.0233
|
0.760
|
| HMC_vs_SMC |
5
|
0.755
|
0.466
|
0.218
|
| Metro_vs_SMC |
0
|
5.034
|
0.000381
|
1.453
|
| Metro_vs_SMC |
1
|
1.473
|
0.169
|
0.425
|
| Metro_vs_SMC |
2
|
3.500
|
0.00497
|
1.010
|
| Metro_vs_SMC |
3
|
6.435
|
4.84e-05
|
1.858
|
| Metro_vs_SMC |
4
|
7.153
|
1.86e-05
|
2.065
|
| Metro_vs_SMC |
5
|
3.952
|
0.00226
|
1.141
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.154 |
0.122 |
0.038 |
0.841 |
| HMC |
2.5 |
0.092 |
0.089 |
0.014 |
0.223 |
| HMC |
3.0 |
0.092 |
0.068 |
0.013 |
1.781 |
| HMC |
4.0 |
0.059 |
0.046 |
0.006 |
2.347 |
| HMC |
10.0 |
0.035 |
0.037 |
0.010 |
-0.190 |
| HMC |
50.0 |
0.030 |
0.028 |
0.006 |
0.360 |
| SMC |
2.1 |
0.123 |
0.122 |
0.038 |
0.011 |
| SMC |
2.5 |
0.085 |
0.089 |
0.014 |
-0.297 |
| SMC |
3.0 |
0.066 |
0.068 |
0.013 |
-0.210 |
| SMC |
4.0 |
0.046 |
0.046 |
0.006 |
0.131 |
| SMC |
10.0 |
0.031 |
0.037 |
0.010 |
-0.547 |
| SMC |
50.0 |
0.028 |
0.028 |
0.006 |
-0.028 |
| Metro |
2.1 |
0.204 |
0.122 |
0.038 |
2.165 |
| Metro |
2.5 |
0.316 |
0.089 |
0.014 |
16.383 |
| Metro |
3.0 |
0.150 |
0.068 |
0.013 |
6.221 |
| Metro |
4.0 |
0.093 |
0.046 |
0.006 |
8.188 |
| Metro |
10.0 |
0.056 |
0.037 |
0.010 |
1.960 |
| Metro |
50.0 |
0.049 |
0.028 |
0.006 |
3.541 |
| DEMetro_Z |
2.1 |
0.268 |
0.122 |
0.038 |
3.856 |
| DEMetro_Z |
2.5 |
0.178 |
0.089 |
0.014 |
6.411 |
| DEMetro_Z |
3.0 |
0.143 |
0.068 |
0.013 |
5.634 |
| DEMetro_Z |
4.0 |
0.093 |
0.046 |
0.006 |
8.247 |
| DEMetro_Z |
10.0 |
0.055 |
0.037 |
0.010 |
1.865 |
| DEMetro_Z |
50.0 |
0.050 |
0.028 |
0.006 |
3.654 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
1.321 |
0.206 |
0.902 |
| HMC |
2.5 |
0.169 |
0.869 |
0.051 |
| HMC |
3.0 |
1.940 |
0.0661 |
0.922 |
| HMC |
4.0 |
1.817 |
0.0834 |
0.829 |
| HMC |
10.0 |
-0.651 |
0.523 |
-0.217 |
| HMC |
50.0 |
0.024 |
0.981 |
0.011 |
| SMC |
2.1 |
0.045 |
0.965 |
0.019 |
| SMC |
2.5 |
-0.491 |
0.629 |
-0.176 |
| SMC |
3.0 |
-0.748 |
0.463 |
-0.370 |
| SMC |
4.0 |
-0.839 |
0.411 |
-0.350 |
| SMC |
10.0 |
-0.916 |
0.371 |
-0.312 |
| SMC |
50.0 |
-0.409 |
0.686 |
-0.173 |
| Metro |
2.1 |
5.762 |
2.52e-05 |
3.586 |
| Metro |
2.5 |
3.364 |
0.00561 |
4.574 |
| Metro |
3.0 |
7.202 |
1.52e-06 |
4.370 |
| Metro |
4.0 |
4.807 |
0.000244 |
3.616 |
| Metro |
10.0 |
3.877 |
0.000813 |
1.592 |
| Metro |
50.0 |
3.186 |
0.00644 |
2.513 |
| DEMetro_Z |
2.1 |
7.210 |
6.08e-06 |
6.764 |
| DEMetro_Z |
2.5 |
4.017 |
0.00166 |
5.133 |
| DEMetro_Z |
3.0 |
5.689 |
7.3e-05 |
5.594 |
| DEMetro_Z |
4.0 |
5.356 |
8.11e-05 |
3.908 |
| DEMetro_Z |
10.0 |
3.110 |
0.00514 |
1.213 |
| DEMetro_Z |
50.0 |
3.611 |
0.00193 |
1.961 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
7.283
|
1.58e-05
|
2.102
|
| DEMetro_Z_vs_SMC |
1
|
4.198
|
0.00149
|
1.212
|
| DEMetro_Z_vs_SMC |
2
|
6.435
|
4.84e-05
|
1.858
|
| DEMetro_Z_vs_SMC |
3
|
5.700
|
0.000138
|
1.645
|
| DEMetro_Z_vs_SMC |
4
|
6.044
|
8.38e-05
|
1.745
|
| DEMetro_Z_vs_SMC |
5
|
3.515
|
0.00484
|
1.015
|
| HMC_vs_Metro |
0
|
-3.445
|
0.00548
|
-0.994
|
| HMC_vs_Metro |
1
|
-3.260
|
0.0076
|
-0.941
|
| HMC_vs_Metro |
2
|
-4.556
|
0.000823
|
-1.315
|
| HMC_vs_Metro |
3
|
-4.244
|
0.00138
|
-1.225
|
| HMC_vs_Metro |
4
|
-5.021
|
0.00039
|
-1.449
|
| HMC_vs_Metro |
5
|
-2.859
|
0.0156
|
-0.825
|
| Metro_vs_DEMetro_Z |
0
|
-2.557
|
0.0267
|
-0.738
|
| Metro_vs_DEMetro_Z |
1
|
-0.255
|
0.803
|
-0.074
|
| Metro_vs_DEMetro_Z |
2
|
-1.086
|
0.301
|
-0.314
|
| Metro_vs_DEMetro_Z |
3
|
-0.257
|
0.802
|
-0.074
|
| Metro_vs_DEMetro_Z |
4
|
0.931
|
0.372
|
0.269
|
| Metro_vs_DEMetro_Z |
5
|
0.751
|
0.469
|
0.217
|
| HMC_vs_SMC |
0
|
1.150
|
0.275
|
0.332
|
| HMC_vs_SMC |
1
|
1.127
|
0.284
|
0.325
|
| HMC_vs_SMC |
2
|
2.842
|
0.016
|
0.820
|
| HMC_vs_SMC |
3
|
2.199
|
0.0501
|
0.635
|
| HMC_vs_SMC |
4
|
0.484
|
0.638
|
0.140
|
| HMC_vs_SMC |
5
|
0.499
|
0.628
|
0.144
|
| Metro_vs_SMC |
0
|
6.332
|
5.58e-05
|
1.828
|
| Metro_vs_SMC |
1
|
3.455
|
0.00538
|
0.997
|
| Metro_vs_SMC |
2
|
8.906
|
2.32e-06
|
2.571
|
| Metro_vs_SMC |
3
|
5.589
|
0.000163
|
1.613
|
| Metro_vs_SMC |
4
|
5.202
|
0.000294
|
1.502
|
| Metro_vs_SMC |
5
|
3.380
|
0.00615
|
0.976
|
| HMC_vs_DEMetro_Z |
0
|
-4.702
|
0.000648
|
-1.357
|
| HMC_vs_DEMetro_Z |
1
|
-4.182
|
0.00153
|
-1.207
|
| HMC_vs_DEMetro_Z |
2
|
-4.834
|
0.000524
|
-1.395
|
| HMC_vs_DEMetro_Z |
3
|
-3.654
|
0.00379
|
-1.055
|
| HMC_vs_DEMetro_Z |
4
|
-4.838
|
0.000521
|
-1.397
|
| HMC_vs_DEMetro_Z |
5
|
-2.644
|
0.0228
|
-0.763
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.018 |
0.014 |
0.004 |
0.902 |
| HMC |
2.5 |
0.015 |
0.015 |
0.004 |
0.051 |
| HMC |
3.0 |
0.019 |
0.015 |
0.004 |
0.922 |
| HMC |
4.0 |
0.017 |
0.014 |
0.004 |
0.829 |
| HMC |
10.0 |
0.013 |
0.015 |
0.006 |
-0.217 |
| HMC |
50.0 |
0.014 |
0.014 |
0.004 |
0.011 |
| SMC |
2.1 |
0.015 |
0.014 |
0.004 |
0.019 |
| SMC |
2.5 |
0.014 |
0.015 |
0.004 |
-0.176 |
| SMC |
3.0 |
0.014 |
0.015 |
0.004 |
-0.370 |
| SMC |
4.0 |
0.013 |
0.014 |
0.004 |
-0.350 |
| SMC |
10.0 |
0.013 |
0.015 |
0.006 |
-0.312 |
| SMC |
50.0 |
0.013 |
0.014 |
0.004 |
-0.173 |
| Metro |
2.1 |
0.030 |
0.014 |
0.004 |
3.586 |
| Metro |
2.5 |
0.035 |
0.015 |
0.004 |
4.574 |
| Metro |
3.0 |
0.033 |
0.015 |
0.004 |
4.370 |
| Metro |
4.0 |
0.027 |
0.014 |
0.004 |
3.616 |
| Metro |
10.0 |
0.024 |
0.015 |
0.006 |
1.592 |
| Metro |
50.0 |
0.024 |
0.014 |
0.004 |
2.513 |
| DEMetro_Z |
2.1 |
0.044 |
0.014 |
0.004 |
6.764 |
| DEMetro_Z |
2.5 |
0.038 |
0.015 |
0.004 |
5.133 |
| DEMetro_Z |
3.0 |
0.037 |
0.015 |
0.004 |
5.594 |
| DEMetro_Z |
4.0 |
0.028 |
0.014 |
0.004 |
3.908 |
| DEMetro_Z |
10.0 |
0.022 |
0.015 |
0.006 |
1.213 |
| DEMetro_Z |
50.0 |
0.022 |
0.014 |
0.004 |
1.961 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
R Hat (scatter)
Mode Transitions
One Chain results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
0.505 |
0.619 |
0.223 |
| HMC |
2.5 |
0.276 |
0.785 |
0.122 |
| HMC |
3.0 |
0.266 |
0.793 |
0.097 |
| HMC |
4.0 |
1.027 |
0.317 |
0.536 |
| HMC |
10.0 |
-1.820 |
0.0843 |
-0.632 |
| HMC |
50.0 |
0.808 |
0.428 |
0.381 |
| SMC |
2.1 |
-0.920 |
0.368 |
-0.347 |
| SMC |
2.5 |
-0.044 |
0.965 |
-0.020 |
| SMC |
3.0 |
-0.849 |
0.405 |
-0.337 |
| SMC |
4.0 |
-0.012 |
0.99 |
-0.005 |
| SMC |
10.0 |
-1.524 |
0.143 |
-0.545 |
| SMC |
50.0 |
1.902 |
0.0705 |
0.735 |
| Metro |
2.1 |
1.524 |
0.145 |
0.872 |
| Metro |
2.5 |
3.885 |
0.002 |
4.350 |
| Metro |
3.0 |
2.269 |
0.0411 |
2.330 |
| Metro |
4.0 |
3.183 |
0.00678 |
2.738 |
| Metro |
10.0 |
1.379 |
0.182 |
0.614 |
| Metro |
50.0 |
3.133 |
0.00583 |
1.792 |
| DEMetro_Z |
2.1 |
3.064 |
0.00773 |
2.151 |
| DEMetro_Z |
2.5 |
3.358 |
0.00459 |
2.684 |
| DEMetro_Z |
3.0 |
2.854 |
0.0119 |
2.004 |
| DEMetro_Z |
4.0 |
4.355 |
0.00071 |
3.879 |
| DEMetro_Z |
10.0 |
1.592 |
0.127 |
0.808 |
| DEMetro_Z |
50.0 |
5.005 |
0.000138 |
3.390 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
-2.908
|
0.0143
|
-0.839
|
| HMC_vs_DEMetro_Z |
1
|
-3.180
|
0.00876
|
-0.918
|
| HMC_vs_DEMetro_Z |
2
|
-2.655
|
0.0224
|
-0.766
|
| HMC_vs_DEMetro_Z |
3
|
-2.964
|
0.0129
|
-0.856
|
| HMC_vs_DEMetro_Z |
4
|
-3.798
|
0.00296
|
-1.096
|
| HMC_vs_DEMetro_Z |
5
|
-4.145
|
0.00163
|
-1.197
|
| Metro_vs_SMC |
0
|
2.251
|
0.0458
|
0.650
|
| Metro_vs_SMC |
1
|
4.261
|
0.00134
|
1.230
|
| Metro_vs_SMC |
2
|
2.520
|
0.0285
|
0.727
|
| Metro_vs_SMC |
3
|
2.970
|
0.0127
|
0.857
|
| Metro_vs_SMC |
4
|
3.801
|
0.00294
|
1.097
|
| Metro_vs_SMC |
5
|
2.419
|
0.0341
|
0.698
|
| Metro_vs_DEMetro_Z |
0
|
-1.652
|
0.127
|
-0.477
|
| Metro_vs_DEMetro_Z |
1
|
1.174
|
0.265
|
0.339
|
| Metro_vs_DEMetro_Z |
2
|
0.268
|
0.794
|
0.077
|
| Metro_vs_DEMetro_Z |
3
|
-1.062
|
0.311
|
-0.307
|
| Metro_vs_DEMetro_Z |
4
|
-0.507
|
0.622
|
-0.146
|
| Metro_vs_DEMetro_Z |
5
|
-1.941
|
0.0783
|
-0.560
|
| HMC_vs_Metro |
0
|
-1.058
|
0.313
|
-0.306
|
| HMC_vs_Metro |
1
|
-3.522
|
0.00478
|
-1.017
|
| HMC_vs_Metro |
2
|
-2.428
|
0.0335
|
-0.701
|
| HMC_vs_Metro |
3
|
-2.266
|
0.0446
|
-0.654
|
| HMC_vs_Metro |
4
|
-4.320
|
0.00121
|
-1.247
|
| HMC_vs_Metro |
5
|
-1.977
|
0.0736
|
-0.571
|
| HMC_vs_SMC |
0
|
1.494
|
0.163
|
0.431
|
| HMC_vs_SMC |
1
|
0.254
|
0.804
|
0.073
|
| HMC_vs_SMC |
2
|
1.174
|
0.265
|
0.339
|
| HMC_vs_SMC |
3
|
1.160
|
0.271
|
0.335
|
| HMC_vs_SMC |
4
|
-0.471
|
0.647
|
-0.136
|
| HMC_vs_SMC |
5
|
-0.758
|
0.464
|
-0.219
|
| DEMetro_Z_vs_SMC |
0
|
4.784
|
0.000568
|
1.381
|
| DEMetro_Z_vs_SMC |
1
|
3.339
|
0.00661
|
0.964
|
| DEMetro_Z_vs_SMC |
2
|
4.005
|
0.00207
|
1.156
|
| DEMetro_Z_vs_SMC |
3
|
4.274
|
0.00131
|
1.234
|
| DEMetro_Z_vs_SMC |
4
|
3.389
|
0.00605
|
0.978
|
| DEMetro_Z_vs_SMC |
5
|
4.036
|
0.00196
|
1.165
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.081 |
0.072 |
0.040 |
0.223 |
| HMC |
2.5 |
0.042 |
0.040 |
0.019 |
0.122 |
| HMC |
3.0 |
0.046 |
0.045 |
0.018 |
0.097 |
| HMC |
4.0 |
0.031 |
0.025 |
0.013 |
0.536 |
| HMC |
10.0 |
0.018 |
0.029 |
0.016 |
-0.632 |
| HMC |
50.0 |
0.020 |
0.016 |
0.010 |
0.381 |
| SMC |
2.1 |
0.058 |
0.072 |
0.040 |
-0.347 |
| SMC |
2.5 |
0.040 |
0.040 |
0.019 |
-0.020 |
| SMC |
3.0 |
0.039 |
0.045 |
0.018 |
-0.337 |
| SMC |
4.0 |
0.025 |
0.025 |
0.013 |
-0.005 |
| SMC |
10.0 |
0.020 |
0.029 |
0.016 |
-0.545 |
| SMC |
50.0 |
0.023 |
0.016 |
0.010 |
0.735 |
| Metro |
2.1 |
0.107 |
0.072 |
0.040 |
0.872 |
| Metro |
2.5 |
0.123 |
0.040 |
0.019 |
4.350 |
| Metro |
3.0 |
0.086 |
0.045 |
0.018 |
2.330 |
| Metro |
4.0 |
0.059 |
0.025 |
0.013 |
2.738 |
| Metro |
10.0 |
0.038 |
0.029 |
0.016 |
0.614 |
| Metro |
50.0 |
0.033 |
0.016 |
0.010 |
1.792 |
| DEMetro_Z |
2.1 |
0.158 |
0.072 |
0.040 |
2.151 |
| DEMetro_Z |
2.5 |
0.091 |
0.040 |
0.019 |
2.684 |
| DEMetro_Z |
3.0 |
0.080 |
0.045 |
0.018 |
2.004 |
| DEMetro_Z |
4.0 |
0.073 |
0.025 |
0.013 |
3.879 |
| DEMetro_Z |
10.0 |
0.041 |
0.029 |
0.016 |
0.808 |
| DEMetro_Z |
50.0 |
0.049 |
0.016 |
0.010 |
3.390 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
0.068 |
0.946 |
0.026 |
| HMC |
2.5 |
-0.872 |
0.393 |
-0.316 |
| HMC |
3.0 |
-0.695 |
0.495 |
-0.260 |
| HMC |
4.0 |
2.798 |
0.0115 |
1.481 |
| HMC |
10.0 |
1.285 |
0.218 |
0.917 |
| HMC |
50.0 |
1.409 |
0.173 |
0.573 |
| SMC |
2.1 |
0.035 |
0.973 |
0.014 |
| SMC |
2.5 |
-1.714 |
0.106 |
-0.548 |
| SMC |
3.0 |
-0.581 |
0.568 |
-0.208 |
| SMC |
4.0 |
1.471 |
0.161 |
0.989 |
| SMC |
10.0 |
2.896 |
0.00839 |
1.218 |
| SMC |
50.0 |
0.998 |
0.329 |
0.389 |
| Metro |
2.1 |
-0.103 |
0.919 |
-0.041 |
| Metro |
2.5 |
0.411 |
0.685 |
0.168 |
| Metro |
3.0 |
1.460 |
0.165 |
1.069 |
| Metro |
4.0 |
3.526 |
0.00285 |
2.355 |
| Metro |
10.0 |
1.984 |
0.07 |
2.396 |
| Metro |
50.0 |
2.082 |
0.053 |
1.281 |
| DEMetro_Z |
2.1 |
-0.164 |
0.871 |
-0.063 |
| DEMetro_Z |
2.5 |
-0.195 |
0.847 |
-0.072 |
| DEMetro_Z |
3.0 |
0.482 |
0.634 |
0.192 |
| DEMetro_Z |
4.0 |
4.106 |
0.00146 |
5.756 |
| DEMetro_Z |
10.0 |
3.661 |
0.00315 |
4.530 |
| DEMetro_Z |
50.0 |
4.222 |
0.000703 |
2.943 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
0.095
|
0.926
|
0.027
|
| HMC_vs_SMC |
1
|
0.793
|
0.444
|
0.229
|
| HMC_vs_SMC |
2
|
-0.848
|
0.414
|
-0.245
|
| HMC_vs_SMC |
3
|
0.618
|
0.549
|
0.179
|
| HMC_vs_SMC |
4
|
-0.437
|
0.671
|
-0.126
|
| HMC_vs_SMC |
5
|
0.421
|
0.682
|
0.121
|
| Metro_vs_DEMetro_Z |
0
|
0.748
|
0.47
|
0.216
|
| Metro_vs_DEMetro_Z |
1
|
0.731
|
0.48
|
0.211
|
| Metro_vs_DEMetro_Z |
2
|
1.208
|
0.252
|
0.349
|
| Metro_vs_DEMetro_Z |
3
|
-2.679
|
0.0215
|
-0.773
|
| Metro_vs_DEMetro_Z |
4
|
-2.071
|
0.0626
|
-0.598
|
| Metro_vs_DEMetro_Z |
5
|
-1.738
|
0.11
|
-0.502
|
| HMC_vs_Metro |
0
|
0.819
|
0.43
|
0.236
|
| HMC_vs_Metro |
1
|
-1.377
|
0.196
|
-0.398
|
| HMC_vs_Metro |
2
|
-1.899
|
0.0841
|
-0.548
|
| HMC_vs_Metro |
3
|
-1.286
|
0.225
|
-0.371
|
| HMC_vs_Metro |
4
|
-1.108
|
0.291
|
-0.320
|
| HMC_vs_Metro |
5
|
-1.271
|
0.23
|
-0.367
|
| HMC_vs_DEMetro_Z |
0
|
1.111
|
0.29
|
0.321
|
| HMC_vs_DEMetro_Z |
1
|
-0.682
|
0.509
|
-0.197
|
| HMC_vs_DEMetro_Z |
2
|
-3.299
|
0.00709
|
-0.952
|
| HMC_vs_DEMetro_Z |
3
|
-2.929
|
0.0137
|
-0.845
|
| HMC_vs_DEMetro_Z |
4
|
-2.428
|
0.0335
|
-0.701
|
| HMC_vs_DEMetro_Z |
5
|
-3.506
|
0.00491
|
-1.012
|
| Metro_vs_SMC |
0
|
-0.577
|
0.575
|
-0.167
|
| Metro_vs_SMC |
1
|
2.474
|
0.0309
|
0.714
|
| Metro_vs_SMC |
2
|
1.922
|
0.0809
|
0.555
|
| Metro_vs_SMC |
3
|
1.387
|
0.193
|
0.401
|
| Metro_vs_SMC |
4
|
1.042
|
0.32
|
0.301
|
| Metro_vs_SMC |
5
|
1.531
|
0.154
|
0.442
|
| DEMetro_Z_vs_SMC |
0
|
-0.784
|
0.45
|
-0.226
|
| DEMetro_Z_vs_SMC |
1
|
1.878
|
0.0871
|
0.542
|
| DEMetro_Z_vs_SMC |
2
|
2.949
|
0.0132
|
0.851
|
| DEMetro_Z_vs_SMC |
3
|
2.978
|
0.0126
|
0.860
|
| DEMetro_Z_vs_SMC |
4
|
3.042
|
0.0112
|
0.878
|
| DEMetro_Z_vs_SMC |
5
|
3.429
|
0.00564
|
0.990
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
9.175 |
8.779 |
15.112 |
0.026 |
| HMC |
2.5 |
1.108 |
1.437 |
1.038 |
-0.316 |
| HMC |
3.0 |
0.489 |
0.730 |
0.925 |
-0.260 |
| HMC |
4.0 |
0.212 |
0.121 |
0.062 |
1.481 |
| HMC |
10.0 |
0.048 |
0.034 |
0.016 |
0.917 |
| HMC |
50.0 |
0.036 |
0.028 |
0.015 |
0.573 |
| SMC |
2.1 |
8.984 |
8.779 |
15.112 |
0.014 |
| SMC |
2.5 |
0.868 |
1.437 |
1.038 |
-0.548 |
| SMC |
3.0 |
0.538 |
0.730 |
0.925 |
-0.208 |
| SMC |
4.0 |
0.182 |
0.121 |
0.062 |
0.989 |
| SMC |
10.0 |
0.053 |
0.034 |
0.016 |
1.218 |
| SMC |
50.0 |
0.033 |
0.028 |
0.015 |
0.389 |
| Metro |
2.1 |
8.166 |
8.779 |
15.112 |
-0.041 |
| Metro |
2.5 |
1.611 |
1.437 |
1.038 |
0.168 |
| Metro |
3.0 |
1.720 |
0.730 |
0.925 |
1.069 |
| Metro |
4.0 |
0.266 |
0.121 |
0.062 |
2.355 |
| Metro |
10.0 |
0.071 |
0.034 |
0.016 |
2.396 |
| Metro |
50.0 |
0.047 |
0.028 |
0.015 |
1.281 |
| DEMetro_Z |
2.1 |
7.831 |
8.779 |
15.112 |
-0.063 |
| DEMetro_Z |
2.5 |
1.361 |
1.437 |
1.038 |
-0.072 |
| DEMetro_Z |
3.0 |
0.908 |
0.730 |
0.925 |
0.192 |
| DEMetro_Z |
4.0 |
0.476 |
0.121 |
0.062 |
5.756 |
| DEMetro_Z |
10.0 |
0.105 |
0.034 |
0.016 |
4.530 |
| DEMetro_Z |
50.0 |
0.072 |
0.028 |
0.015 |
2.943 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
2.842 |
0.00966 |
1.274 |
| HMC |
2.5 |
1.488 |
0.151 |
0.662 |
| HMC |
3.0 |
1.704 |
0.105 |
0.584 |
| HMC |
4.0 |
3.225 |
0.00538 |
2.165 |
| HMC |
10.0 |
-0.991 |
0.337 |
-0.315 |
| HMC |
50.0 |
0.871 |
0.394 |
0.441 |
| SMC |
2.1 |
0.208 |
0.837 |
0.088 |
| SMC |
2.5 |
-0.521 |
0.608 |
-0.243 |
| SMC |
3.0 |
1.162 |
0.258 |
0.460 |
| SMC |
4.0 |
0.611 |
0.549 |
0.342 |
| SMC |
10.0 |
-0.607 |
0.551 |
-0.210 |
| SMC |
50.0 |
1.202 |
0.242 |
0.520 |
| Metro |
2.1 |
3.682 |
0.00187 |
2.244 |
| Metro |
2.5 |
4.274 |
0.00107 |
5.719 |
| Metro |
3.0 |
5.192 |
0.000178 |
5.288 |
| Metro |
4.0 |
5.901 |
5.82e-05 |
6.411 |
| Metro |
10.0 |
3.989 |
0.000778 |
2.082 |
| Metro |
50.0 |
4.508 |
0.000309 |
2.713 |
| DEMetro_Z |
2.1 |
4.561 |
0.000411 |
3.535 |
| DEMetro_Z |
2.5 |
6.691 |
8.98e-06 |
5.242 |
| DEMetro_Z |
3.0 |
8.801 |
3.98e-08 |
4.634 |
| DEMetro_Z |
4.0 |
8.670 |
1.68e-06 |
12.249 |
| DEMetro_Z |
10.0 |
5.894 |
9.74e-06 |
2.967 |
| DEMetro_Z |
50.0 |
6.869 |
7.52e-06 |
5.627 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
-1.742
|
0.109
|
-0.503
|
| Metro_vs_DEMetro_Z |
1
|
0.285
|
0.781
|
0.082
|
| Metro_vs_DEMetro_Z |
2
|
0.603
|
0.559
|
0.174
|
| Metro_vs_DEMetro_Z |
3
|
-5.978
|
9.22e-05
|
-1.726
|
| Metro_vs_DEMetro_Z |
4
|
-1.718
|
0.114
|
-0.496
|
| Metro_vs_DEMetro_Z |
5
|
-3.256
|
0.00765
|
-0.940
|
| DEMetro_Z_vs_SMC |
0
|
5.589
|
0.000163
|
1.613
|
| DEMetro_Z_vs_SMC |
1
|
6.117
|
7.55e-05
|
1.766
|
| DEMetro_Z_vs_SMC |
2
|
7.587
|
1.08e-05
|
2.190
|
| DEMetro_Z_vs_SMC |
3
|
8.110
|
5.73e-06
|
2.341
|
| DEMetro_Z_vs_SMC |
4
|
8.736
|
2.8e-06
|
2.522
|
| DEMetro_Z_vs_SMC |
5
|
5.825
|
0.000115
|
1.681
|
| HMC_vs_DEMetro_Z |
0
|
-3.282
|
0.00731
|
-0.947
|
| HMC_vs_DEMetro_Z |
1
|
-5.629
|
0.000154
|
-1.625
|
| HMC_vs_DEMetro_Z |
2
|
-9.361
|
1.42e-06
|
-2.702
|
| HMC_vs_DEMetro_Z |
3
|
-6.150
|
7.21e-05
|
-1.775
|
| HMC_vs_DEMetro_Z |
4
|
-8.808
|
2.59e-06
|
-2.543
|
| HMC_vs_DEMetro_Z |
5
|
-5.624
|
0.000155
|
-1.623
|
| HMC_vs_Metro |
0
|
-1.513
|
0.159
|
-0.437
|
| HMC_vs_Metro |
1
|
-4.273
|
0.00131
|
-1.234
|
| HMC_vs_Metro |
2
|
-4.960
|
0.000429
|
-1.432
|
| HMC_vs_Metro |
3
|
-3.658
|
0.00377
|
-1.056
|
| HMC_vs_Metro |
4
|
-5.515
|
0.000182
|
-1.592
|
| HMC_vs_Metro |
5
|
-3.409
|
0.00584
|
-0.984
|
| HMC_vs_SMC |
0
|
3.246
|
0.00779
|
0.937
|
| HMC_vs_SMC |
1
|
1.920
|
0.0811
|
0.554
|
| HMC_vs_SMC |
2
|
0.367
|
0.721
|
0.106
|
| HMC_vs_SMC |
3
|
2.648
|
0.0226
|
0.765
|
| HMC_vs_SMC |
4
|
-0.507
|
0.622
|
-0.146
|
| HMC_vs_SMC |
5
|
-0.138
|
0.892
|
-0.040
|
| Metro_vs_SMC |
0
|
5.687
|
0.000141
|
1.642
|
| Metro_vs_SMC |
1
|
5.087
|
0.000351
|
1.468
|
| Metro_vs_SMC |
2
|
5.109
|
0.000339
|
1.475
|
| Metro_vs_SMC |
3
|
5.528
|
0.000179
|
1.596
|
| Metro_vs_SMC |
4
|
6.276
|
6.03e-05
|
1.812
|
| Metro_vs_SMC |
5
|
4.352
|
0.00115
|
1.256
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.170 |
0.122 |
0.038 |
1.274 |
| HMC |
2.5 |
0.098 |
0.089 |
0.014 |
0.662 |
| HMC |
3.0 |
0.076 |
0.068 |
0.013 |
0.584 |
| HMC |
4.0 |
0.058 |
0.046 |
0.006 |
2.165 |
| HMC |
10.0 |
0.034 |
0.037 |
0.010 |
-0.315 |
| HMC |
50.0 |
0.031 |
0.028 |
0.006 |
0.441 |
| SMC |
2.1 |
0.125 |
0.122 |
0.038 |
0.088 |
| SMC |
2.5 |
0.086 |
0.089 |
0.014 |
-0.243 |
| SMC |
3.0 |
0.075 |
0.068 |
0.013 |
0.460 |
| SMC |
4.0 |
0.048 |
0.046 |
0.006 |
0.342 |
| SMC |
10.0 |
0.035 |
0.037 |
0.010 |
-0.210 |
| SMC |
50.0 |
0.031 |
0.028 |
0.006 |
0.520 |
| Metro |
2.1 |
0.207 |
0.122 |
0.038 |
2.244 |
| Metro |
2.5 |
0.168 |
0.089 |
0.014 |
5.719 |
| Metro |
3.0 |
0.138 |
0.068 |
0.013 |
5.288 |
| Metro |
4.0 |
0.083 |
0.046 |
0.006 |
6.411 |
| Metro |
10.0 |
0.057 |
0.037 |
0.010 |
2.082 |
| Metro |
50.0 |
0.044 |
0.028 |
0.006 |
2.713 |
| DEMetro_Z |
2.1 |
0.255 |
0.122 |
0.038 |
3.535 |
| DEMetro_Z |
2.5 |
0.161 |
0.089 |
0.014 |
5.242 |
| DEMetro_Z |
3.0 |
0.130 |
0.068 |
0.013 |
4.634 |
| DEMetro_Z |
4.0 |
0.116 |
0.046 |
0.006 |
12.249 |
| DEMetro_Z |
10.0 |
0.066 |
0.037 |
0.010 |
2.967 |
| DEMetro_Z |
50.0 |
0.062 |
0.028 |
0.006 |
5.627 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
2.075 |
0.0537 |
1.285 |
| HMC |
2.5 |
1.456 |
0.16 |
0.609 |
| HMC |
3.0 |
1.867 |
0.0753 |
0.777 |
| HMC |
4.0 |
1.427 |
0.17 |
0.739 |
| HMC |
10.0 |
-0.283 |
0.781 |
-0.093 |
| HMC |
50.0 |
0.659 |
0.517 |
0.296 |
| SMC |
2.1 |
1.299 |
0.208 |
0.581 |
| SMC |
2.5 |
0.302 |
0.766 |
0.142 |
| SMC |
3.0 |
3.008 |
0.00661 |
1.343 |
| SMC |
4.0 |
-1.003 |
0.327 |
-0.394 |
| SMC |
10.0 |
-0.145 |
0.886 |
-0.049 |
| SMC |
50.0 |
0.412 |
0.684 |
0.162 |
| Metro |
2.1 |
4.244 |
0.000937 |
4.097 |
| Metro |
2.5 |
5.842 |
9.48e-06 |
2.809 |
| Metro |
3.0 |
3.643 |
0.0027 |
3.081 |
| Metro |
4.0 |
3.169 |
0.00623 |
2.222 |
| Metro |
10.0 |
4.174 |
0.000407 |
1.835 |
| Metro |
50.0 |
3.429 |
0.00313 |
2.017 |
| DEMetro_Z |
2.1 |
7.415 |
1.8e-06 |
5.119 |
| DEMetro_Z |
2.5 |
4.220 |
0.000433 |
2.127 |
| DEMetro_Z |
3.0 |
5.543 |
2.72e-05 |
3.043 |
| DEMetro_Z |
4.0 |
5.653 |
6.79e-05 |
5.055 |
| DEMetro_Z |
10.0 |
3.706 |
0.00128 |
1.671 |
| DEMetro_Z |
50.0 |
5.790 |
3.7e-05 |
4.271 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
7.289
|
1.57e-05
|
2.104
|
| DEMetro_Z_vs_SMC |
1
|
3.106
|
0.00999
|
0.897
|
| DEMetro_Z_vs_SMC |
2
|
2.382
|
0.0364
|
0.688
|
| DEMetro_Z_vs_SMC |
3
|
6.331
|
5.59e-05
|
1.828
|
| DEMetro_Z_vs_SMC |
4
|
4.905
|
0.000468
|
1.416
|
| DEMetro_Z_vs_SMC |
5
|
5.175
|
0.000306
|
1.494
|
| HMC_vs_Metro |
0
|
-2.659
|
0.0222
|
-0.768
|
| HMC_vs_Metro |
1
|
-5.172
|
0.000308
|
-1.493
|
| HMC_vs_Metro |
2
|
-2.783
|
0.0178
|
-0.803
|
| HMC_vs_Metro |
3
|
-2.348
|
0.0386
|
-0.678
|
| HMC_vs_Metro |
4
|
-5.383
|
0.000222
|
-1.554
|
| HMC_vs_Metro |
5
|
-2.714
|
0.0201
|
-0.784
|
| Metro_vs_DEMetro_Z |
0
|
-1.079
|
0.304
|
-0.311
|
| Metro_vs_DEMetro_Z |
1
|
1.171
|
0.266
|
0.338
|
| Metro_vs_DEMetro_Z |
2
|
0.049
|
0.962
|
0.014
|
| Metro_vs_DEMetro_Z |
3
|
-3.436
|
0.00556
|
-0.992
|
| Metro_vs_DEMetro_Z |
4
|
0.357
|
0.728
|
0.103
|
| Metro_vs_DEMetro_Z |
5
|
-2.762
|
0.0185
|
-0.797
|
| HMC_vs_SMC |
0
|
1.258
|
0.234
|
0.363
|
| HMC_vs_SMC |
1
|
0.891
|
0.392
|
0.257
|
| HMC_vs_SMC |
2
|
-1.187
|
0.26
|
-0.343
|
| HMC_vs_SMC |
3
|
2.900
|
0.0145
|
0.837
|
| HMC_vs_SMC |
4
|
-0.195
|
0.849
|
-0.056
|
| HMC_vs_SMC |
5
|
0.304
|
0.767
|
0.088
|
| Metro_vs_SMC |
0
|
4.073
|
0.00184
|
1.176
|
| Metro_vs_SMC |
1
|
4.345
|
0.00117
|
1.254
|
| Metro_vs_SMC |
2
|
1.993
|
0.0717
|
0.575
|
| Metro_vs_SMC |
3
|
4.647
|
0.000708
|
1.342
|
| Metro_vs_SMC |
4
|
6.462
|
4.66e-05
|
1.866
|
| Metro_vs_SMC |
5
|
3.999
|
0.00209
|
1.155
|
| HMC_vs_DEMetro_Z |
0
|
-4.438
|
0.000999
|
-1.281
|
| HMC_vs_DEMetro_Z |
1
|
-2.519
|
0.0285
|
-0.727
|
| HMC_vs_DEMetro_Z |
2
|
-4.661
|
0.000692
|
-1.346
|
| HMC_vs_DEMetro_Z |
3
|
-5.136
|
0.000325
|
-1.483
|
| HMC_vs_DEMetro_Z |
4
|
-5.694
|
0.000139
|
-1.644
|
| HMC_vs_DEMetro_Z |
5
|
-5.083
|
0.000353
|
-1.467
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.020 |
0.014 |
0.004 |
1.285 |
| HMC |
2.5 |
0.018 |
0.015 |
0.004 |
0.609 |
| HMC |
3.0 |
0.018 |
0.015 |
0.004 |
0.777 |
| HMC |
4.0 |
0.017 |
0.014 |
0.004 |
0.739 |
| HMC |
10.0 |
0.014 |
0.015 |
0.006 |
-0.093 |
| HMC |
50.0 |
0.015 |
0.014 |
0.004 |
0.296 |
| SMC |
2.1 |
0.017 |
0.014 |
0.004 |
0.581 |
| SMC |
2.5 |
0.016 |
0.015 |
0.004 |
0.142 |
| SMC |
3.0 |
0.021 |
0.015 |
0.004 |
1.343 |
| SMC |
4.0 |
0.013 |
0.014 |
0.004 |
-0.394 |
| SMC |
10.0 |
0.014 |
0.015 |
0.006 |
-0.049 |
| SMC |
50.0 |
0.014 |
0.014 |
0.004 |
0.162 |
| Metro |
2.1 |
0.032 |
0.014 |
0.004 |
4.097 |
| Metro |
2.5 |
0.028 |
0.015 |
0.004 |
2.809 |
| Metro |
3.0 |
0.027 |
0.015 |
0.004 |
3.081 |
| Metro |
4.0 |
0.022 |
0.014 |
0.004 |
2.222 |
| Metro |
10.0 |
0.026 |
0.015 |
0.006 |
1.835 |
| Metro |
50.0 |
0.022 |
0.014 |
0.004 |
2.017 |
| DEMetro_Z |
2.1 |
0.037 |
0.014 |
0.004 |
5.119 |
| DEMetro_Z |
2.5 |
0.025 |
0.015 |
0.004 |
2.127 |
| DEMetro_Z |
3.0 |
0.027 |
0.015 |
0.004 |
3.043 |
| DEMetro_Z |
4.0 |
0.032 |
0.014 |
0.004 |
5.055 |
| DEMetro_Z |
10.0 |
0.025 |
0.015 |
0.006 |
1.671 |
| DEMetro_Z |
50.0 |
0.032 |
0.014 |
0.004 |
4.271 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
Mode Transitions
KDE + Init Plots
Forest & Ridge Plots
Pooled
Chain
Pairwise Scatter Plots
Pooled
Chain
Varying_only_Mode_distance
(Mixture,
mm,
12 runs)
Pooled Chains results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
4.412 |
0.000458 |
2.986 |
| HMC |
8 |
4.943 |
0.000433 |
26.334 |
| HMC |
10 |
4.192 |
0.0015 |
73.125 |
| HMC |
12 |
4.894 |
0.000469 |
26.636 |
| HMC |
15 |
3.935 |
0.00232 |
40.401 |
| HMC |
18 |
4.105 |
0.00172 |
18.745 |
| SMC |
5 |
-2.230 |
0.0403 |
-0.718 |
| SMC |
8 |
0.281 |
0.781 |
0.121 |
| SMC |
10 |
1.743 |
0.101 |
1.176 |
| SMC |
12 |
0.577 |
0.57 |
0.217 |
| SMC |
15 |
-0.121 |
0.905 |
-0.055 |
| SMC |
18 |
0.016 |
0.988 |
0.005 |
| Metro |
5 |
1.573 |
0.134 |
0.928 |
| Metro |
8 |
4.142 |
0.00158 |
12.886 |
| Metro |
10 |
3.886 |
0.00253 |
38.310 |
| Metro |
12 |
4.722 |
0.00062 |
30.101 |
| Metro |
15 |
4.841 |
0.000515 |
40.205 |
| Metro |
18 |
2.562 |
0.0263 |
12.699 |
| DEMetro_Z |
5 |
2.477 |
0.0223 |
1.217 |
| DEMetro_Z |
8 |
4.151 |
0.00148 |
8.426 |
| DEMetro_Z |
10 |
3.864 |
0.00263 |
49.270 |
| DEMetro_Z |
12 |
4.478 |
0.000919 |
22.146 |
| DEMetro_Z |
15 |
4.577 |
0.000791 |
45.000 |
| DEMetro_Z |
18 |
4.190 |
0.00146 |
13.559 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
3.191
|
0.00859
|
0.921
|
| HMC_vs_DEMetro_Z |
1
|
2.816
|
0.0168
|
0.813
|
| HMC_vs_DEMetro_Z |
2
|
1.545
|
0.151
|
0.446
|
| HMC_vs_DEMetro_Z |
3
|
0.731
|
0.48
|
0.211
|
| HMC_vs_DEMetro_Z |
4
|
-0.473
|
0.645
|
-0.137
|
| HMC_vs_DEMetro_Z |
5
|
1.161
|
0.27
|
0.335
|
| Metro_vs_SMC |
0
|
2.715
|
0.0201
|
0.784
|
| Metro_vs_SMC |
1
|
4.278
|
0.0013
|
1.235
|
| Metro_vs_SMC |
2
|
3.706
|
0.00347
|
1.070
|
| Metro_vs_SMC |
3
|
4.744
|
0.000606
|
1.369
|
| Metro_vs_SMC |
4
|
4.784
|
0.000568
|
1.381
|
| Metro_vs_SMC |
5
|
2.528
|
0.0281
|
0.730
|
| Metro_vs_DEMetro_Z |
0
|
-0.537
|
0.602
|
-0.155
|
| Metro_vs_DEMetro_Z |
1
|
1.854
|
0.0907
|
0.535
|
| Metro_vs_DEMetro_Z |
2
|
-0.575
|
0.577
|
-0.166
|
| Metro_vs_DEMetro_Z |
3
|
1.072
|
0.307
|
0.309
|
| Metro_vs_DEMetro_Z |
4
|
-0.490
|
0.634
|
-0.141
|
| Metro_vs_DEMetro_Z |
5
|
-0.204
|
0.842
|
-0.059
|
| HMC_vs_Metro |
0
|
2.900
|
0.0144
|
0.837
|
| HMC_vs_Metro |
1
|
2.122
|
0.0574
|
0.613
|
| HMC_vs_Metro |
2
|
1.611
|
0.136
|
0.465
|
| HMC_vs_Metro |
3
|
-0.593
|
0.565
|
-0.171
|
| HMC_vs_Metro |
4
|
0.032
|
0.975
|
0.009
|
| HMC_vs_Metro |
5
|
1.924
|
0.0806
|
0.555
|
| HMC_vs_SMC |
0
|
5.795
|
0.00012
|
1.673
|
| HMC_vs_SMC |
1
|
4.798
|
0.000555
|
1.385
|
| HMC_vs_SMC |
2
|
4.127
|
0.00168
|
1.191
|
| HMC_vs_SMC |
3
|
4.916
|
0.00046
|
1.419
|
| HMC_vs_SMC |
4
|
3.872
|
0.0026
|
1.118
|
| HMC_vs_SMC |
5
|
4.060
|
0.00188
|
1.172
|
| DEMetro_Z_vs_SMC |
0
|
4.139
|
0.00165
|
1.195
|
| DEMetro_Z_vs_SMC |
1
|
4.481
|
0.000929
|
1.294
|
| DEMetro_Z_vs_SMC |
2
|
3.744
|
0.00324
|
1.081
|
| DEMetro_Z_vs_SMC |
3
|
4.401
|
0.00106
|
1.271
|
| DEMetro_Z_vs_SMC |
4
|
4.483
|
0.000927
|
1.294
|
| DEMetro_Z_vs_SMC |
5
|
4.175
|
0.00155
|
1.205
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
0.137 |
0.049 |
0.030 |
2.986 |
| HMC |
8 |
1.175 |
0.063 |
0.042 |
26.334 |
| HMC |
10 |
1.808 |
0.042 |
0.024 |
73.125 |
| HMC |
12 |
1.772 |
0.075 |
0.064 |
26.636 |
| HMC |
15 |
2.242 |
0.099 |
0.053 |
40.401 |
| HMC |
18 |
2.456 |
0.111 |
0.125 |
18.745 |
| SMC |
5 |
0.027 |
0.049 |
0.030 |
-0.718 |
| SMC |
8 |
0.069 |
0.063 |
0.042 |
0.121 |
| SMC |
10 |
0.071 |
0.042 |
0.024 |
1.176 |
| SMC |
12 |
0.089 |
0.075 |
0.064 |
0.217 |
| SMC |
15 |
0.096 |
0.099 |
0.053 |
-0.055 |
| SMC |
18 |
0.112 |
0.111 |
0.125 |
0.005 |
| Metro |
5 |
0.076 |
0.049 |
0.030 |
0.928 |
| Metro |
8 |
0.607 |
0.063 |
0.042 |
12.886 |
| Metro |
10 |
0.967 |
0.042 |
0.024 |
38.310 |
| Metro |
12 |
1.993 |
0.075 |
0.064 |
30.101 |
| Metro |
15 |
2.231 |
0.099 |
0.053 |
40.205 |
| Metro |
18 |
1.699 |
0.111 |
0.125 |
12.699 |
| DEMetro_Z |
5 |
0.085 |
0.049 |
0.030 |
1.217 |
| DEMetro_Z |
8 |
0.419 |
0.063 |
0.042 |
8.426 |
| DEMetro_Z |
10 |
1.232 |
0.042 |
0.024 |
49.270 |
| DEMetro_Z |
12 |
1.486 |
0.075 |
0.064 |
22.146 |
| DEMetro_Z |
15 |
2.486 |
0.099 |
0.053 |
45.000 |
| DEMetro_Z |
18 |
1.807 |
0.111 |
0.125 |
13.559 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
0.196 |
0.847 |
0.070 |
| HMC |
8 |
3.513 |
0.00484 |
35.458 |
| HMC |
10 |
3.261 |
0.00758 |
130.694 |
| HMC |
12 |
3.294 |
0.00715 |
86.122 |
| HMC |
15 |
2.818 |
0.0167 |
83.299 |
| HMC |
18 |
2.907 |
0.0143 |
82.090 |
| SMC |
5 |
-0.133 |
0.896 |
-0.045 |
| SMC |
8 |
1.111 |
0.281 |
0.591 |
| SMC |
10 |
0.873 |
0.395 |
0.528 |
| SMC |
12 |
0.940 |
0.358 |
0.435 |
| SMC |
15 |
-1.718 |
0.1 |
-0.655 |
| SMC |
18 |
-0.511 |
0.614 |
-0.216 |
| Metro |
5 |
1.413 |
0.176 |
0.852 |
| Metro |
8 |
3.046 |
0.0109 |
9.389 |
| Metro |
10 |
2.365 |
0.0375 |
38.420 |
| Metro |
12 |
3.267 |
0.0075 |
111.721 |
| Metro |
15 |
3.300 |
0.00708 |
72.228 |
| Metro |
18 |
2.023 |
0.0681 |
60.816 |
| DEMetro_Z |
5 |
0.601 |
0.554 |
0.230 |
| DEMetro_Z |
8 |
2.792 |
0.0166 |
4.593 |
| DEMetro_Z |
10 |
2.408 |
0.0347 |
63.999 |
| DEMetro_Z |
12 |
3.153 |
0.00919 |
62.378 |
| DEMetro_Z |
15 |
3.237 |
0.00792 |
92.831 |
| DEMetro_Z |
18 |
3.714 |
0.00341 |
43.992 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
0.360
|
0.725
|
0.104
|
| HMC_vs_SMC |
1
|
3.515
|
0.00484
|
1.015
|
| HMC_vs_SMC |
2
|
3.222
|
0.00814
|
0.930
|
| HMC_vs_SMC |
3
|
3.293
|
0.00717
|
0.951
|
| HMC_vs_SMC |
4
|
2.848
|
0.0159
|
0.822
|
| HMC_vs_SMC |
5
|
2.909
|
0.0142
|
0.840
|
| Metro_vs_DEMetro_Z |
0
|
1.052
|
0.315
|
0.304
|
| Metro_vs_DEMetro_Z |
1
|
1.561
|
0.147
|
0.451
|
| Metro_vs_DEMetro_Z |
2
|
-0.743
|
0.473
|
-0.214
|
| Metro_vs_DEMetro_Z |
3
|
1.229
|
0.245
|
0.355
|
| Metro_vs_DEMetro_Z |
4
|
-0.607
|
0.556
|
-0.175
|
| Metro_vs_DEMetro_Z |
5
|
0.646
|
0.531
|
0.187
|
| HMC_vs_Metro |
0
|
-1.384
|
0.194
|
-0.399
|
| HMC_vs_Metro |
1
|
2.339
|
0.0393
|
0.675
|
| HMC_vs_Metro |
2
|
2.018
|
0.0687
|
0.583
|
| HMC_vs_Metro |
3
|
-0.701
|
0.498
|
-0.202
|
| HMC_vs_Metro |
4
|
0.560
|
0.587
|
0.162
|
| HMC_vs_Metro |
5
|
1.831
|
0.0943
|
0.529
|
| HMC_vs_DEMetro_Z |
0
|
-0.464
|
0.652
|
-0.134
|
| HMC_vs_DEMetro_Z |
1
|
2.855
|
0.0157
|
0.824
|
| HMC_vs_DEMetro_Z |
2
|
2.117
|
0.0579
|
0.611
|
| HMC_vs_DEMetro_Z |
3
|
0.790
|
0.446
|
0.228
|
| HMC_vs_DEMetro_Z |
4
|
-0.326
|
0.751
|
-0.094
|
| HMC_vs_DEMetro_Z |
5
|
1.463
|
0.172
|
0.422
|
| Metro_vs_SMC |
0
|
1.582
|
0.142
|
0.457
|
| Metro_vs_SMC |
1
|
2.756
|
0.0187
|
0.796
|
| Metro_vs_SMC |
2
|
2.383
|
0.0363
|
0.688
|
| Metro_vs_SMC |
3
|
3.249
|
0.00775
|
0.938
|
| Metro_vs_SMC |
4
|
3.348
|
0.00651
|
0.966
|
| Metro_vs_SMC |
5
|
2.027
|
0.0676
|
0.585
|
| DEMetro_Z_vs_SMC |
0
|
0.974
|
0.351
|
0.281
|
| DEMetro_Z_vs_SMC |
1
|
2.134
|
0.0562
|
0.616
|
| DEMetro_Z_vs_SMC |
2
|
2.366
|
0.0374
|
0.683
|
| DEMetro_Z_vs_SMC |
3
|
3.132
|
0.00955
|
0.904
|
| DEMetro_Z_vs_SMC |
4
|
3.254
|
0.00768
|
0.939
|
| DEMetro_Z_vs_SMC |
5
|
3.700
|
0.0035
|
1.068
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
0.070 |
0.066 |
0.058 |
0.070 |
| HMC |
8 |
2.808 |
0.094 |
0.077 |
35.458 |
| HMC |
10 |
7.441 |
0.089 |
0.056 |
130.694 |
| HMC |
12 |
6.419 |
0.111 |
0.073 |
86.122 |
| HMC |
15 |
11.637 |
0.245 |
0.137 |
83.299 |
| HMC |
18 |
13.138 |
0.204 |
0.158 |
82.090 |
| SMC |
5 |
0.063 |
0.066 |
0.058 |
-0.045 |
| SMC |
8 |
0.139 |
0.094 |
0.077 |
0.591 |
| SMC |
10 |
0.118 |
0.089 |
0.056 |
0.528 |
| SMC |
12 |
0.143 |
0.111 |
0.073 |
0.435 |
| SMC |
15 |
0.156 |
0.245 |
0.137 |
-0.655 |
| SMC |
18 |
0.170 |
0.204 |
0.158 |
-0.216 |
| Metro |
5 |
0.115 |
0.066 |
0.058 |
0.852 |
| Metro |
8 |
0.812 |
0.094 |
0.077 |
9.389 |
| Metro |
10 |
2.250 |
0.089 |
0.056 |
38.420 |
| Metro |
12 |
8.294 |
0.111 |
0.073 |
111.721 |
| Metro |
15 |
10.123 |
0.245 |
0.137 |
72.228 |
| Metro |
18 |
9.786 |
0.204 |
0.158 |
60.816 |
| DEMetro_Z |
5 |
0.079 |
0.066 |
0.058 |
0.230 |
| DEMetro_Z |
8 |
0.445 |
0.094 |
0.077 |
4.593 |
| DEMetro_Z |
10 |
3.689 |
0.089 |
0.056 |
63.999 |
| DEMetro_Z |
12 |
4.680 |
0.111 |
0.073 |
62.378 |
| DEMetro_Z |
15 |
12.941 |
0.245 |
0.137 |
92.831 |
| DEMetro_Z |
18 |
7.135 |
0.204 |
0.158 |
43.992 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
4.375 |
0.000661 |
3.759 |
| HMC |
8 |
4.696 |
0.000646 |
28.716 |
| HMC |
10 |
4.102 |
0.00175 |
92.662 |
| HMC |
12 |
4.917 |
0.000453 |
29.384 |
| HMC |
15 |
3.916 |
0.0024 |
45.277 |
| HMC |
18 |
3.984 |
0.00212 |
22.049 |
| SMC |
5 |
-2.577 |
0.0201 |
-0.834 |
| SMC |
8 |
0.380 |
0.708 |
0.145 |
| SMC |
10 |
2.314 |
0.0345 |
1.546 |
| SMC |
12 |
0.280 |
0.782 |
0.105 |
| SMC |
15 |
-0.525 |
0.605 |
-0.225 |
| SMC |
18 |
0.050 |
0.961 |
0.016 |
| Metro |
5 |
1.883 |
0.079 |
1.348 |
| Metro |
8 |
4.139 |
0.0016 |
13.863 |
| Metro |
10 |
3.756 |
0.00317 |
45.463 |
| Metro |
12 |
4.632 |
0.00072 |
33.675 |
| Metro |
15 |
4.960 |
0.000426 |
44.703 |
| Metro |
18 |
2.577 |
0.0256 |
14.127 |
| DEMetro_Z |
5 |
4.223 |
0.000475 |
2.264 |
| DEMetro_Z |
8 |
4.322 |
0.00111 |
8.986 |
| DEMetro_Z |
10 |
3.745 |
0.00323 |
61.268 |
| DEMetro_Z |
12 |
4.418 |
0.00102 |
25.482 |
| DEMetro_Z |
15 |
4.658 |
0.000694 |
49.158 |
| DEMetro_Z |
18 |
4.168 |
0.00153 |
15.685 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
-1.267
|
0.231
|
-0.366
|
| Metro_vs_DEMetro_Z |
1
|
1.779
|
0.103
|
0.514
|
| Metro_vs_DEMetro_Z |
2
|
-0.656
|
0.525
|
-0.189
|
| Metro_vs_DEMetro_Z |
3
|
0.921
|
0.377
|
0.266
|
| Metro_vs_DEMetro_Z |
4
|
-0.434
|
0.673
|
-0.125
|
| Metro_vs_DEMetro_Z |
5
|
-0.311
|
0.762
|
-0.090
|
| DEMetro_Z_vs_SMC |
0
|
5.865
|
0.000108
|
1.693
|
| DEMetro_Z_vs_SMC |
1
|
4.532
|
0.000854
|
1.308
|
| DEMetro_Z_vs_SMC |
2
|
3.625
|
0.00399
|
1.046
|
| DEMetro_Z_vs_SMC |
3
|
4.369
|
0.00112
|
1.261
|
| DEMetro_Z_vs_SMC |
4
|
4.607
|
0.000756
|
1.330
|
| DEMetro_Z_vs_SMC |
5
|
4.161
|
0.00159
|
1.201
|
| HMC_vs_DEMetro_Z |
0
|
1.853
|
0.0908
|
0.535
|
| HMC_vs_DEMetro_Z |
1
|
2.746
|
0.019
|
0.793
|
| HMC_vs_DEMetro_Z |
2
|
1.569
|
0.145
|
0.453
|
| HMC_vs_DEMetro_Z |
3
|
0.535
|
0.604
|
0.154
|
| HMC_vs_DEMetro_Z |
4
|
-0.358
|
0.727
|
-0.103
|
| HMC_vs_DEMetro_Z |
5
|
1.107
|
0.292
|
0.320
|
| HMC_vs_Metro |
0
|
2.603
|
0.0246
|
0.751
|
| HMC_vs_Metro |
1
|
2.062
|
0.0636
|
0.595
|
| HMC_vs_Metro |
2
|
1.699
|
0.117
|
0.490
|
| HMC_vs_Metro |
3
|
-0.638
|
0.536
|
-0.184
|
| HMC_vs_Metro |
4
|
0.080
|
0.938
|
0.023
|
| HMC_vs_Metro |
5
|
2.111
|
0.0584
|
0.609
|
| HMC_vs_SMC |
0
|
5.345
|
0.000236
|
1.543
|
| HMC_vs_SMC |
1
|
4.618
|
0.000743
|
1.333
|
| HMC_vs_SMC |
2
|
4.047
|
0.00192
|
1.168
|
| HMC_vs_SMC |
3
|
4.965
|
0.000426
|
1.433
|
| HMC_vs_SMC |
4
|
3.889
|
0.00252
|
1.123
|
| HMC_vs_SMC |
5
|
3.943
|
0.0023
|
1.138
|
| Metro_vs_SMC |
0
|
2.877
|
0.0151
|
0.830
|
| Metro_vs_SMC |
1
|
4.243
|
0.00138
|
1.225
|
| Metro_vs_SMC |
2
|
3.596
|
0.0042
|
1.038
|
| Metro_vs_SMC |
3
|
4.662
|
0.000691
|
1.346
|
| Metro_vs_SMC |
4
|
4.934
|
0.000447
|
1.424
|
| Metro_vs_SMC |
5
|
2.541
|
0.0274
|
0.734
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
0.133 |
0.059 |
0.020 |
3.759 |
| HMC |
8 |
1.070 |
0.074 |
0.035 |
28.716 |
| HMC |
10 |
1.689 |
0.054 |
0.018 |
92.662 |
| HMC |
12 |
1.581 |
0.083 |
0.051 |
29.384 |
| HMC |
15 |
2.063 |
0.111 |
0.043 |
45.277 |
| HMC |
18 |
2.304 |
0.117 |
0.099 |
22.049 |
| SMC |
5 |
0.042 |
0.059 |
0.020 |
-0.834 |
| SMC |
8 |
0.079 |
0.074 |
0.035 |
0.145 |
| SMC |
10 |
0.081 |
0.054 |
0.018 |
1.546 |
| SMC |
12 |
0.088 |
0.083 |
0.051 |
0.105 |
| SMC |
15 |
0.101 |
0.111 |
0.043 |
-0.225 |
| SMC |
18 |
0.118 |
0.117 |
0.099 |
0.016 |
| Metro |
5 |
0.086 |
0.059 |
0.020 |
1.348 |
| Metro |
8 |
0.555 |
0.074 |
0.035 |
13.863 |
| Metro |
10 |
0.856 |
0.054 |
0.018 |
45.463 |
| Metro |
12 |
1.799 |
0.083 |
0.051 |
33.675 |
| Metro |
15 |
2.038 |
0.111 |
0.043 |
44.703 |
| Metro |
18 |
1.518 |
0.117 |
0.099 |
14.127 |
| DEMetro_Z |
5 |
0.104 |
0.059 |
0.020 |
2.264 |
| DEMetro_Z |
8 |
0.386 |
0.074 |
0.035 |
8.986 |
| DEMetro_Z |
10 |
1.135 |
0.054 |
0.018 |
61.268 |
| DEMetro_Z |
12 |
1.382 |
0.083 |
0.051 |
25.482 |
| DEMetro_Z |
15 |
2.230 |
0.111 |
0.043 |
49.158 |
| DEMetro_Z |
18 |
1.673 |
0.117 |
0.099 |
15.685 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
4.716 |
0.000359 |
4.185 |
| HMC |
8 |
4.870 |
0.000489 |
31.545 |
| HMC |
10 |
4.266 |
0.00133 |
81.453 |
| HMC |
12 |
5.060 |
0.000361 |
31.448 |
| HMC |
15 |
4.030 |
0.00198 |
54.169 |
| HMC |
18 |
4.059 |
0.00187 |
22.645 |
| SMC |
5 |
-2.286 |
0.0332 |
-0.817 |
| SMC |
8 |
0.581 |
0.567 |
0.243 |
| SMC |
10 |
1.829 |
0.0867 |
1.252 |
| SMC |
12 |
0.524 |
0.605 |
0.208 |
| SMC |
15 |
-0.054 |
0.957 |
-0.025 |
| SMC |
18 |
-0.091 |
0.929 |
-0.029 |
| Metro |
5 |
2.020 |
0.0612 |
1.413 |
| Metro |
8 |
3.970 |
0.00215 |
15.154 |
| Metro |
10 |
3.934 |
0.00233 |
43.625 |
| Metro |
12 |
4.952 |
0.00043 |
34.682 |
| Metro |
15 |
4.939 |
0.000441 |
54.482 |
| Metro |
18 |
2.607 |
0.0243 |
15.246 |
| DEMetro_Z |
5 |
3.521 |
0.00275 |
2.229 |
| DEMetro_Z |
8 |
4.070 |
0.00175 |
9.824 |
| DEMetro_Z |
10 |
3.986 |
0.00213 |
56.481 |
| DEMetro_Z |
12 |
4.526 |
0.000853 |
26.290 |
| DEMetro_Z |
15 |
4.880 |
0.000486 |
59.439 |
| DEMetro_Z |
18 |
4.251 |
0.00133 |
16.816 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
4.307
|
0.00124
|
1.243
|
| DEMetro_Z_vs_SMC |
1
|
4.174
|
0.00155
|
1.205
|
| DEMetro_Z_vs_SMC |
2
|
3.877
|
0.00258
|
1.119
|
| DEMetro_Z_vs_SMC |
3
|
4.463
|
0.000957
|
1.288
|
| DEMetro_Z_vs_SMC |
4
|
4.799
|
0.000554
|
1.385
|
| DEMetro_Z_vs_SMC |
5
|
4.269
|
0.00132
|
1.232
|
| HMC_vs_Metro |
0
|
3.045
|
0.0111
|
0.879
|
| HMC_vs_Metro |
1
|
2.134
|
0.0562
|
0.616
|
| HMC_vs_Metro |
2
|
1.593
|
0.14
|
0.460
|
| HMC_vs_Metro |
3
|
-0.501
|
0.626
|
-0.145
|
| HMC_vs_Metro |
4
|
-0.039
|
0.97
|
-0.011
|
| HMC_vs_Metro |
5
|
1.992
|
0.0717
|
0.575
|
| Metro_vs_DEMetro_Z |
0
|
-1.063
|
0.311
|
-0.307
|
| Metro_vs_DEMetro_Z |
1
|
1.765
|
0.105
|
0.510
|
| Metro_vs_DEMetro_Z |
2
|
-0.603
|
0.559
|
-0.174
|
| Metro_vs_DEMetro_Z |
3
|
1.023
|
0.328
|
0.295
|
| Metro_vs_DEMetro_Z |
4
|
-0.412
|
0.688
|
-0.119
|
| Metro_vs_DEMetro_Z |
5
|
-0.307
|
0.764
|
-0.089
|
| HMC_vs_SMC |
0
|
5.392
|
0.000219
|
1.557
|
| HMC_vs_SMC |
1
|
4.764
|
0.000586
|
1.375
|
| HMC_vs_SMC |
2
|
4.209
|
0.00146
|
1.215
|
| HMC_vs_SMC |
3
|
5.085
|
0.000352
|
1.468
|
| HMC_vs_SMC |
4
|
3.982
|
0.00215
|
1.149
|
| HMC_vs_SMC |
5
|
4.035
|
0.00196
|
1.165
|
| Metro_vs_SMC |
0
|
2.872
|
0.0152
|
0.829
|
| Metro_vs_SMC |
1
|
4.019
|
0.00202
|
1.160
|
| Metro_vs_SMC |
2
|
3.794
|
0.00297
|
1.095
|
| Metro_vs_SMC |
3
|
4.977
|
0.000417
|
1.437
|
| Metro_vs_SMC |
4
|
4.894
|
0.000476
|
1.413
|
| Metro_vs_SMC |
5
|
2.594
|
0.0249
|
0.749
|
| HMC_vs_DEMetro_Z |
0
|
2.263
|
0.0449
|
0.653
|
| HMC_vs_DEMetro_Z |
1
|
2.847
|
0.0159
|
0.822
|
| HMC_vs_DEMetro_Z |
2
|
1.482
|
0.166
|
0.428
|
| HMC_vs_DEMetro_Z |
3
|
0.718
|
0.488
|
0.207
|
| HMC_vs_DEMetro_Z |
4
|
-0.418
|
0.684
|
-0.121
|
| HMC_vs_DEMetro_Z |
5
|
1.055
|
0.314
|
0.304
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
0.041 |
0.016 |
0.006 |
4.185 |
| HMC |
8 |
0.255 |
0.014 |
0.008 |
31.545 |
| HMC |
10 |
0.318 |
0.008 |
0.004 |
81.453 |
| HMC |
12 |
0.268 |
0.011 |
0.008 |
31.448 |
| HMC |
15 |
0.273 |
0.011 |
0.005 |
54.169 |
| HMC |
18 |
0.248 |
0.011 |
0.010 |
22.645 |
| SMC |
5 |
0.011 |
0.016 |
0.006 |
-0.817 |
| SMC |
8 |
0.016 |
0.014 |
0.008 |
0.243 |
| SMC |
10 |
0.013 |
0.008 |
0.004 |
1.252 |
| SMC |
12 |
0.012 |
0.011 |
0.008 |
0.208 |
| SMC |
15 |
0.011 |
0.011 |
0.005 |
-0.025 |
| SMC |
18 |
0.011 |
0.011 |
0.010 |
-0.029 |
| Metro |
5 |
0.024 |
0.016 |
0.006 |
1.413 |
| Metro |
8 |
0.130 |
0.014 |
0.008 |
15.154 |
| Metro |
10 |
0.174 |
0.008 |
0.004 |
43.625 |
| Metro |
12 |
0.294 |
0.011 |
0.008 |
34.682 |
| Metro |
15 |
0.275 |
0.011 |
0.005 |
54.482 |
| Metro |
18 |
0.170 |
0.011 |
0.010 |
15.246 |
| DEMetro_Z |
5 |
0.029 |
0.016 |
0.006 |
2.229 |
| DEMetro_Z |
8 |
0.089 |
0.014 |
0.008 |
9.824 |
| DEMetro_Z |
10 |
0.223 |
0.008 |
0.004 |
56.481 |
| DEMetro_Z |
12 |
0.226 |
0.011 |
0.008 |
26.290 |
| DEMetro_Z |
15 |
0.299 |
0.011 |
0.005 |
59.439 |
| DEMetro_Z |
18 |
0.187 |
0.011 |
0.010 |
16.816 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
R Hat (scatter)
Mode Transitions
One Chain results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
4.160 |
0.00102 |
3.649 |
| HMC |
8 |
4.025 |
0.00199 |
30.056 |
| HMC |
10 |
226.759 |
5.03e-30 |
144.252 |
| HMC |
12 |
165.418 |
2.1e-35 |
65.305 |
| HMC |
15 |
195.478 |
6.36e-34 |
98.100 |
| HMC |
18 |
116.183 |
6.72e-32 |
50.088 |
| SMC |
5 |
-1.834 |
0.0855 |
-0.588 |
| SMC |
8 |
-0.198 |
0.845 |
-0.066 |
| SMC |
10 |
0.872 |
0.395 |
0.476 |
| SMC |
12 |
-0.295 |
0.771 |
-0.106 |
| SMC |
15 |
1.138 |
0.269 |
0.590 |
| SMC |
18 |
1.147 |
0.264 |
0.442 |
| Metro |
5 |
2.702 |
0.0158 |
1.790 |
| Metro |
8 |
3.195 |
0.00831 |
8.605 |
| Metro |
10 |
4.613 |
0.000748 |
83.311 |
| Metro |
12 |
27.159 |
1.09e-11 |
62.270 |
| Metro |
15 |
192.652 |
2.13e-33 |
98.396 |
| Metro |
18 |
115.751 |
7.6e-32 |
49.996 |
| DEMetro_Z |
5 |
2.350 |
0.0306 |
1.349 |
| DEMetro_Z |
8 |
2.467 |
0.0311 |
11.636 |
| DEMetro_Z |
10 |
5.607 |
0.000158 |
98.720 |
| DEMetro_Z |
12 |
5.012 |
0.000393 |
44.369 |
| DEMetro_Z |
15 |
8.454 |
3.81e-06 |
84.169 |
| DEMetro_Z |
18 |
119.486 |
2.2e-32 |
49.968 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
2.381
|
0.0364
|
0.687
|
| HMC_vs_DEMetro_Z |
1
|
1.897
|
0.0844
|
0.548
|
| HMC_vs_DEMetro_Z |
2
|
2.574
|
0.0259
|
0.743
|
| HMC_vs_DEMetro_Z |
3
|
2.358
|
0.0379
|
0.681
|
| HMC_vs_DEMetro_Z |
4
|
1.424
|
0.182
|
0.411
|
| HMC_vs_DEMetro_Z |
5
|
0.325
|
0.752
|
0.094
|
| Metro_vs_SMC |
0
|
4.320
|
0.00121
|
1.247
|
| Metro_vs_SMC |
1
|
3.340
|
0.0066
|
0.964
|
| Metro_vs_SMC |
2
|
4.583
|
0.000786
|
1.323
|
| Metro_vs_SMC |
3
|
25.793
|
3.44e-11
|
7.446
|
| Metro_vs_SMC |
4
|
175.890
|
2.52e-20
|
50.775
|
| Metro_vs_SMC |
5
|
118.417
|
1.95e-18
|
34.184
|
| Metro_vs_DEMetro_Z |
0
|
0.556
|
0.59
|
0.160
|
| Metro_vs_DEMetro_Z |
1
|
-0.477
|
0.643
|
-0.138
|
| Metro_vs_DEMetro_Z |
2
|
-0.573
|
0.578
|
-0.165
|
| Metro_vs_DEMetro_Z |
3
|
2.209
|
0.0493
|
0.638
|
| Metro_vs_DEMetro_Z |
4
|
1.444
|
0.176
|
0.417
|
| Metro_vs_DEMetro_Z |
5
|
0.080
|
0.938
|
0.023
|
| HMC_vs_Metro |
0
|
2.475
|
0.0309
|
0.714
|
| HMC_vs_Metro |
1
|
2.571
|
0.026
|
0.742
|
| HMC_vs_Metro |
2
|
3.424
|
0.00569
|
0.988
|
| HMC_vs_Metro |
3
|
1.349
|
0.204
|
0.389
|
| HMC_vs_Metro |
4
|
-1.850
|
0.0914
|
-0.534
|
| HMC_vs_Metro |
5
|
0.752
|
0.468
|
0.217
|
| HMC_vs_SMC |
0
|
5.241
|
0.000276
|
1.513
|
| HMC_vs_SMC |
1
|
4.049
|
0.00192
|
1.169
|
| HMC_vs_SMC |
2
|
182.426
|
1.68e-20
|
52.662
|
| HMC_vs_SMC |
3
|
176.638
|
2.4e-20
|
50.991
|
| HMC_vs_SMC |
4
|
162.486
|
6.01e-20
|
46.906
|
| HMC_vs_SMC |
5
|
120.182
|
1.66e-18
|
34.694
|
| DEMetro_Z_vs_SMC |
0
|
4.310
|
0.00123
|
1.244
|
| DEMetro_Z_vs_SMC |
1
|
2.460
|
0.0317
|
0.710
|
| DEMetro_Z_vs_SMC |
2
|
5.530
|
0.000178
|
1.596
|
| DEMetro_Z_vs_SMC |
3
|
4.951
|
0.000435
|
1.429
|
| DEMetro_Z_vs_SMC |
4
|
8.377
|
4.21e-06
|
2.418
|
| DEMetro_Z_vs_SMC |
5
|
123.276
|
1.25e-18
|
35.587
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
0.157 |
0.049 |
0.030 |
3.649 |
| HMC |
8 |
1.332 |
0.063 |
0.042 |
30.056 |
| HMC |
10 |
3.525 |
0.042 |
0.024 |
144.252 |
| HMC |
12 |
4.236 |
0.075 |
0.064 |
65.305 |
| HMC |
15 |
5.302 |
0.099 |
0.053 |
98.100 |
| HMC |
18 |
6.376 |
0.111 |
0.125 |
50.088 |
| SMC |
5 |
0.031 |
0.049 |
0.030 |
-0.588 |
| SMC |
8 |
0.061 |
0.063 |
0.042 |
-0.066 |
| SMC |
10 |
0.054 |
0.042 |
0.024 |
0.476 |
| SMC |
12 |
0.069 |
0.075 |
0.064 |
-0.106 |
| SMC |
15 |
0.130 |
0.099 |
0.053 |
0.590 |
| SMC |
18 |
0.166 |
0.111 |
0.125 |
0.442 |
| Metro |
5 |
0.102 |
0.049 |
0.030 |
1.790 |
| Metro |
8 |
0.427 |
0.063 |
0.042 |
8.605 |
| Metro |
10 |
2.054 |
0.042 |
0.024 |
83.311 |
| Metro |
12 |
4.043 |
0.075 |
0.064 |
62.270 |
| Metro |
15 |
5.318 |
0.099 |
0.053 |
98.396 |
| Metro |
18 |
6.364 |
0.111 |
0.125 |
49.996 |
| DEMetro_Z |
5 |
0.089 |
0.049 |
0.030 |
1.349 |
| DEMetro_Z |
8 |
0.555 |
0.063 |
0.042 |
11.636 |
| DEMetro_Z |
10 |
2.426 |
0.042 |
0.024 |
98.720 |
| DEMetro_Z |
12 |
2.902 |
0.075 |
0.064 |
44.369 |
| DEMetro_Z |
15 |
4.563 |
0.099 |
0.053 |
84.169 |
| DEMetro_Z |
18 |
6.361 |
0.111 |
0.125 |
49.968 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
0.539 |
0.595 |
0.203 |
| HMC |
8 |
2.814 |
0.0168 |
53.023 |
| HMC |
10 |
540.545 |
1.54e-38 |
312.694 |
| HMC |
12 |
551.289 |
1.29e-36 |
346.369 |
| HMC |
15 |
659.625 |
4.87e-48 |
288.854 |
| HMC |
18 |
856.075 |
4.82e-51 |
361.964 |
| SMC |
5 |
-0.149 |
0.883 |
-0.061 |
| SMC |
8 |
-0.050 |
0.961 |
-0.021 |
| SMC |
10 |
0.839 |
0.413 |
0.509 |
| SMC |
12 |
0.716 |
0.482 |
0.369 |
| SMC |
15 |
-1.197 |
0.244 |
-0.451 |
| SMC |
18 |
-0.068 |
0.946 |
-0.032 |
| Metro |
5 |
2.112 |
0.0494 |
1.233 |
| Metro |
8 |
2.312 |
0.0406 |
5.872 |
| Metro |
10 |
3.769 |
0.0031 |
157.935 |
| Metro |
12 |
16.014 |
5.68e-09 |
319.954 |
| Metro |
15 |
696.699 |
3.06e-49 |
288.913 |
| Metro |
18 |
919.373 |
1.14e-51 |
361.917 |
| DEMetro_Z |
5 |
2.026 |
0.0572 |
1.073 |
| DEMetro_Z |
8 |
1.993 |
0.0715 |
14.295 |
| DEMetro_Z |
10 |
5.200 |
0.000295 |
195.095 |
| DEMetro_Z |
12 |
4.733 |
0.000616 |
231.670 |
| DEMetro_Z |
15 |
7.597 |
1.06e-05 |
241.747 |
| DEMetro_Z |
18 |
795.045 |
6.82e-49 |
362.003 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
0.909
|
0.383
|
0.262
|
| HMC_vs_SMC |
1
|
2.837
|
0.0162
|
0.819
|
| HMC_vs_SMC |
2
|
667.254
|
1.08e-26
|
192.620
|
| HMC_vs_SMC |
3
|
642.666
|
1.63e-26
|
185.522
|
| HMC_vs_SMC |
4
|
712.510
|
5.23e-27
|
205.684
|
| HMC_vs_SMC |
5
|
1143.449
|
2.88e-29
|
330.085
|
| Metro_vs_DEMetro_Z |
0
|
0.350
|
0.733
|
0.101
|
| Metro_vs_DEMetro_Z |
1
|
-1.006
|
0.336
|
-0.290
|
| Metro_vs_DEMetro_Z |
2
|
-0.598
|
0.562
|
-0.172
|
| Metro_vs_DEMetro_Z |
3
|
1.899
|
0.0841
|
0.548
|
| Metro_vs_DEMetro_Z |
4
|
1.486
|
0.165
|
0.429
|
| Metro_vs_DEMetro_Z |
5
|
-0.824
|
0.428
|
-0.238
|
| HMC_vs_Metro |
0
|
-1.873
|
0.0878
|
-0.541
|
| HMC_vs_Metro |
1
|
2.421
|
0.034
|
0.699
|
| HMC_vs_Metro |
2
|
3.718
|
0.00339
|
1.073
|
| HMC_vs_Metro |
3
|
1.342
|
0.207
|
0.387
|
| HMC_vs_Metro |
4
|
-0.612
|
0.553
|
-0.177
|
| HMC_vs_Metro |
5
|
0.684
|
0.508
|
0.197
|
| HMC_vs_DEMetro_Z |
0
|
-1.746
|
0.109
|
-0.504
|
| HMC_vs_DEMetro_Z |
1
|
1.766
|
0.105
|
0.510
|
| HMC_vs_DEMetro_Z |
2
|
3.125
|
0.00966
|
0.902
|
| HMC_vs_DEMetro_Z |
3
|
2.342
|
0.0391
|
0.676
|
| HMC_vs_DEMetro_Z |
4
|
1.484
|
0.166
|
0.428
|
| HMC_vs_DEMetro_Z |
5
|
-0.585
|
0.57
|
-0.169
|
| Metro_vs_SMC |
0
|
1.940
|
0.0785
|
0.560
|
| Metro_vs_SMC |
1
|
2.230
|
0.0475
|
0.644
|
| Metro_vs_SMC |
2
|
3.772
|
0.00309
|
1.089
|
| Metro_vs_SMC |
3
|
16.058
|
5.55e-09
|
4.635
|
| Metro_vs_SMC |
4
|
786.504
|
1.76e-27
|
227.044
|
| Metro_vs_SMC |
5
|
1287.879
|
7.77e-30
|
371.779
|
| DEMetro_Z_vs_SMC |
0
|
1.980
|
0.0732
|
0.572
|
| DEMetro_Z_vs_SMC |
1
|
1.970
|
0.0745
|
0.569
|
| DEMetro_Z_vs_SMC |
2
|
5.158
|
0.000314
|
1.489
|
| DEMetro_Z_vs_SMC |
3
|
4.738
|
0.000611
|
1.368
|
| DEMetro_Z_vs_SMC |
4
|
7.585
|
1.08e-05
|
2.190
|
| DEMetro_Z_vs_SMC |
5
|
1111.850
|
3.91e-29
|
320.963
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
0.077 |
0.066 |
0.058 |
0.203 |
| HMC |
8 |
4.152 |
0.094 |
0.077 |
53.023 |
| HMC |
10 |
17.680 |
0.089 |
0.056 |
312.694 |
| HMC |
12 |
25.480 |
0.111 |
0.073 |
346.369 |
| HMC |
15 |
39.748 |
0.245 |
0.137 |
288.854 |
| HMC |
18 |
57.234 |
0.204 |
0.158 |
361.964 |
| SMC |
5 |
0.062 |
0.066 |
0.058 |
-0.061 |
| SMC |
8 |
0.092 |
0.094 |
0.077 |
-0.021 |
| SMC |
10 |
0.117 |
0.089 |
0.056 |
0.509 |
| SMC |
12 |
0.138 |
0.111 |
0.073 |
0.369 |
| SMC |
15 |
0.183 |
0.245 |
0.137 |
-0.451 |
| SMC |
18 |
0.199 |
0.204 |
0.158 |
-0.032 |
| Metro |
5 |
0.138 |
0.066 |
0.058 |
1.233 |
| Metro |
8 |
0.543 |
0.094 |
0.077 |
5.872 |
| Metro |
10 |
8.974 |
0.089 |
0.056 |
157.935 |
| Metro |
12 |
23.546 |
0.111 |
0.073 |
319.954 |
| Metro |
15 |
39.756 |
0.245 |
0.137 |
288.913 |
| Metro |
18 |
57.227 |
0.204 |
0.158 |
361.917 |
| DEMetro_Z |
5 |
0.128 |
0.066 |
0.058 |
1.073 |
| DEMetro_Z |
8 |
1.188 |
0.094 |
0.077 |
14.295 |
| DEMetro_Z |
10 |
11.064 |
0.089 |
0.056 |
195.095 |
| DEMetro_Z |
12 |
17.079 |
0.111 |
0.073 |
231.670 |
| DEMetro_Z |
15 |
33.306 |
0.245 |
0.137 |
241.747 |
| DEMetro_Z |
18 |
57.241 |
0.204 |
0.158 |
362.003 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
4.229 |
0.00104 |
4.610 |
| HMC |
8 |
3.920 |
0.00238 |
32.317 |
| HMC |
10 |
42.245 |
1.28e-13 |
178.506 |
| HMC |
12 |
34.801 |
5.66e-13 |
71.024 |
| HMC |
15 |
36.608 |
4.88e-13 |
104.228 |
| HMC |
18 |
37.400 |
1.18e-13 |
56.388 |
| SMC |
5 |
-2.150 |
0.0481 |
-0.679 |
| SMC |
8 |
-0.296 |
0.77 |
-0.100 |
| SMC |
10 |
1.474 |
0.159 |
0.891 |
| SMC |
12 |
0.077 |
0.939 |
0.028 |
| SMC |
15 |
0.826 |
0.419 |
0.449 |
| SMC |
18 |
1.051 |
0.305 |
0.403 |
| Metro |
5 |
3.488 |
0.00336 |
2.592 |
| Metro |
8 |
3.328 |
0.00657 |
9.803 |
| Metro |
10 |
4.506 |
0.000892 |
105.693 |
| Metro |
12 |
26.195 |
1.84e-11 |
66.954 |
| Metro |
15 |
47.503 |
1.87e-14 |
103.819 |
| Metro |
18 |
55.523 |
9.2e-17 |
56.330 |
| DEMetro_Z |
5 |
4.187 |
0.000651 |
2.614 |
| DEMetro_Z |
8 |
2.669 |
0.0217 |
12.524 |
| DEMetro_Z |
10 |
5.577 |
0.000166 |
117.886 |
| DEMetro_Z |
12 |
5.042 |
0.000375 |
49.496 |
| DEMetro_Z |
15 |
8.377 |
4.17e-06 |
93.009 |
| DEMetro_Z |
18 |
49.948 |
8.82e-16 |
56.742 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
-0.025
|
0.98
|
-0.007
|
| Metro_vs_DEMetro_Z |
1
|
-0.417
|
0.685
|
-0.120
|
| Metro_vs_DEMetro_Z |
2
|
-0.382
|
0.71
|
-0.110
|
| Metro_vs_DEMetro_Z |
3
|
1.968
|
0.0748
|
0.568
|
| Metro_vs_DEMetro_Z |
4
|
0.944
|
0.366
|
0.272
|
| Metro_vs_DEMetro_Z |
5
|
-0.261
|
0.799
|
-0.075
|
| DEMetro_Z_vs_SMC |
0
|
5.972
|
9.29e-05
|
1.724
|
| DEMetro_Z_vs_SMC |
1
|
2.658
|
0.0223
|
0.767
|
| DEMetro_Z_vs_SMC |
2
|
5.465
|
0.000196
|
1.577
|
| DEMetro_Z_vs_SMC |
3
|
4.972
|
0.000421
|
1.435
|
| DEMetro_Z_vs_SMC |
4
|
8.324
|
4.47e-06
|
2.403
|
| DEMetro_Z_vs_SMC |
5
|
46.967
|
4.99e-14
|
13.558
|
| HMC_vs_DEMetro_Z |
0
|
1.743
|
0.109
|
0.503
|
| HMC_vs_DEMetro_Z |
1
|
1.882
|
0.0865
|
0.543
|
| HMC_vs_DEMetro_Z |
2
|
2.733
|
0.0195
|
0.789
|
| HMC_vs_DEMetro_Z |
3
|
2.210
|
0.0492
|
0.638
|
| HMC_vs_DEMetro_Z |
4
|
1.072
|
0.307
|
0.309
|
| HMC_vs_DEMetro_Z |
5
|
-0.180
|
0.86
|
-0.052
|
| HMC_vs_Metro |
0
|
1.955
|
0.0765
|
0.564
|
| HMC_vs_Metro |
1
|
2.441
|
0.0328
|
0.705
|
| HMC_vs_Metro |
2
|
3.000
|
0.0121
|
0.866
|
| HMC_vs_Metro |
3
|
1.158
|
0.272
|
0.334
|
| HMC_vs_Metro |
4
|
0.101
|
0.921
|
0.029
|
| HMC_vs_Metro |
5
|
0.032
|
0.975
|
0.009
|
| HMC_vs_SMC |
0
|
5.139
|
0.000324
|
1.484
|
| HMC_vs_SMC |
1
|
3.961
|
0.00223
|
1.143
|
| HMC_vs_SMC |
2
|
40.843
|
2.3e-13
|
11.790
|
| HMC_vs_SMC |
3
|
35.557
|
1.05e-12
|
10.265
|
| HMC_vs_SMC |
4
|
33.910
|
1.76e-12
|
9.789
|
| HMC_vs_SMC |
5
|
39.509
|
3.31e-13
|
11.405
|
| Metro_vs_SMC |
0
|
4.899
|
0.000472
|
1.414
|
| Metro_vs_SMC |
1
|
3.446
|
0.00546
|
0.995
|
| Metro_vs_SMC |
2
|
4.472
|
0.000944
|
1.291
|
| Metro_vs_SMC |
3
|
24.697
|
5.5e-11
|
7.129
|
| Metro_vs_SMC |
4
|
50.559
|
2.23e-14
|
14.595
|
| Metro_vs_SMC |
5
|
52.817
|
1.38e-14
|
15.247
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
0.150 |
0.059 |
0.020 |
4.610 |
| HMC |
8 |
1.195 |
0.074 |
0.035 |
32.317 |
| HMC |
10 |
3.203 |
0.054 |
0.018 |
178.506 |
| HMC |
12 |
3.703 |
0.083 |
0.051 |
71.024 |
| HMC |
15 |
4.604 |
0.111 |
0.043 |
104.228 |
| HMC |
18 |
5.710 |
0.117 |
0.099 |
56.388 |
| SMC |
5 |
0.045 |
0.059 |
0.020 |
-0.679 |
| SMC |
8 |
0.070 |
0.074 |
0.035 |
-0.100 |
| SMC |
10 |
0.070 |
0.054 |
0.018 |
0.891 |
| SMC |
12 |
0.084 |
0.083 |
0.051 |
0.028 |
| SMC |
15 |
0.130 |
0.111 |
0.043 |
0.449 |
| SMC |
18 |
0.157 |
0.117 |
0.099 |
0.403 |
| Metro |
5 |
0.110 |
0.059 |
0.020 |
2.592 |
| Metro |
8 |
0.414 |
0.074 |
0.035 |
9.803 |
| Metro |
10 |
1.919 |
0.054 |
0.018 |
105.693 |
| Metro |
12 |
3.496 |
0.083 |
0.051 |
66.954 |
| Metro |
15 |
4.586 |
0.111 |
0.043 |
103.819 |
| Metro |
18 |
5.705 |
0.117 |
0.099 |
56.330 |
| DEMetro_Z |
5 |
0.111 |
0.059 |
0.020 |
2.614 |
| DEMetro_Z |
8 |
0.508 |
0.074 |
0.035 |
12.524 |
| DEMetro_Z |
10 |
2.134 |
0.054 |
0.018 |
117.886 |
| DEMetro_Z |
12 |
2.606 |
0.083 |
0.051 |
49.496 |
| DEMetro_Z |
15 |
4.120 |
0.111 |
0.043 |
93.009 |
| DEMetro_Z |
18 |
5.745 |
0.117 |
0.099 |
56.742 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
4.190 |
0.00119 |
5.149 |
| HMC |
8 |
4.026 |
0.00199 |
35.713 |
| HMC |
10 |
80.982 |
3.38e-17 |
159.269 |
| HMC |
12 |
119.856 |
7.25e-26 |
74.448 |
| HMC |
15 |
100.182 |
3.2e-19 |
124.666 |
| HMC |
18 |
105.160 |
4.34e-27 |
57.316 |
| SMC |
5 |
-2.067 |
0.0529 |
-0.706 |
| SMC |
8 |
-0.160 |
0.874 |
-0.055 |
| SMC |
10 |
1.378 |
0.185 |
0.765 |
| SMC |
12 |
0.060 |
0.953 |
0.021 |
| SMC |
15 |
1.404 |
0.179 |
0.893 |
| SMC |
18 |
1.249 |
0.225 |
0.480 |
| Metro |
5 |
3.534 |
0.00317 |
2.751 |
| Metro |
8 |
3.295 |
0.00698 |
10.204 |
| Metro |
10 |
4.688 |
0.000662 |
93.520 |
| Metro |
12 |
28.542 |
6.95e-12 |
71.702 |
| Metro |
15 |
130.830 |
8.44e-22 |
127.493 |
| Metro |
18 |
90.624 |
2.28e-23 |
58.307 |
| DEMetro_Z |
5 |
3.408 |
0.00384 |
2.425 |
| DEMetro_Z |
8 |
2.507 |
0.0291 |
14.750 |
| DEMetro_Z |
10 |
5.641 |
0.000151 |
109.951 |
| DEMetro_Z |
12 |
5.108 |
0.000338 |
51.048 |
| DEMetro_Z |
15 |
8.640 |
3.1e-06 |
105.803 |
| DEMetro_Z |
18 |
100.998 |
5.7e-26 |
57.632 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
4.816
|
0.000539
|
1.390
|
| DEMetro_Z_vs_SMC |
1
|
2.491
|
0.03
|
0.719
|
| DEMetro_Z_vs_SMC |
2
|
5.532
|
0.000178
|
1.597
|
| DEMetro_Z_vs_SMC |
3
|
5.050
|
0.000372
|
1.458
|
| DEMetro_Z_vs_SMC |
4
|
8.528
|
3.54e-06
|
2.462
|
| DEMetro_Z_vs_SMC |
5
|
104.653
|
7.58e-18
|
30.211
|
| HMC_vs_Metro |
0
|
2.087
|
0.0609
|
0.603
|
| HMC_vs_Metro |
1
|
2.603
|
0.0246
|
0.751
|
| HMC_vs_Metro |
2
|
3.543
|
0.00461
|
1.023
|
| HMC_vs_Metro |
3
|
1.209
|
0.252
|
0.349
|
| HMC_vs_Metro |
4
|
-2.183
|
0.0516
|
-0.630
|
| HMC_vs_Metro |
5
|
-1.655
|
0.126
|
-0.478
|
| Metro_vs_DEMetro_Z |
0
|
0.344
|
0.737
|
0.099
|
| Metro_vs_DEMetro_Z |
1
|
-0.589
|
0.568
|
-0.170
|
| Metro_vs_DEMetro_Z |
2
|
-0.562
|
0.585
|
-0.162
|
| Metro_vs_DEMetro_Z |
3
|
2.259
|
0.0451
|
0.652
|
| Metro_vs_DEMetro_Z |
4
|
1.790
|
0.101
|
0.517
|
| Metro_vs_DEMetro_Z |
5
|
0.724
|
0.484
|
0.209
|
| HMC_vs_SMC |
0
|
5.034
|
0.000382
|
1.453
|
| HMC_vs_SMC |
1
|
4.053
|
0.00191
|
1.170
|
| HMC_vs_SMC |
2
|
83.457
|
9.11e-17
|
24.092
|
| HMC_vs_SMC |
3
|
120.156
|
1.66e-18
|
34.686
|
| HMC_vs_SMC |
4
|
91.885
|
3.17e-17
|
26.525
|
| HMC_vs_SMC |
5
|
117.868
|
2.05e-18
|
34.026
|
| Metro_vs_SMC |
0
|
4.620
|
0.00074
|
1.334
|
| Metro_vs_SMC |
1
|
3.387
|
0.00606
|
0.978
|
| Metro_vs_SMC |
2
|
4.665
|
0.000688
|
1.347
|
| Metro_vs_SMC |
3
|
27.480
|
1.73e-11
|
7.933
|
| Metro_vs_SMC |
4
|
129.149
|
7.51e-19
|
37.282
|
| Metro_vs_SMC |
5
|
81.885
|
1.12e-16
|
23.638
|
| HMC_vs_DEMetro_Z |
0
|
2.152
|
0.0544
|
0.621
|
| HMC_vs_DEMetro_Z |
1
|
1.775
|
0.104
|
0.512
|
| HMC_vs_DEMetro_Z |
2
|
2.488
|
0.0302
|
0.718
|
| HMC_vs_DEMetro_Z |
3
|
2.323
|
0.0404
|
0.670
|
| HMC_vs_DEMetro_Z |
4
|
1.640
|
0.129
|
0.473
|
| HMC_vs_DEMetro_Z |
5
|
-0.425
|
0.679
|
-0.123
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
0.046 |
0.016 |
0.006 |
5.149 |
| HMC |
8 |
0.287 |
0.014 |
0.008 |
35.713 |
| HMC |
10 |
0.615 |
0.008 |
0.004 |
159.269 |
| HMC |
12 |
0.620 |
0.011 |
0.008 |
74.448 |
| HMC |
15 |
0.615 |
0.011 |
0.005 |
124.666 |
| HMC |
18 |
0.610 |
0.011 |
0.010 |
57.316 |
| SMC |
5 |
0.011 |
0.016 |
0.006 |
-0.706 |
| SMC |
8 |
0.014 |
0.014 |
0.008 |
-0.055 |
| SMC |
10 |
0.011 |
0.008 |
0.004 |
0.765 |
| SMC |
12 |
0.011 |
0.011 |
0.008 |
0.021 |
| SMC |
15 |
0.015 |
0.011 |
0.005 |
0.893 |
| SMC |
18 |
0.016 |
0.011 |
0.010 |
0.480 |
| Metro |
5 |
0.032 |
0.016 |
0.006 |
2.751 |
| Metro |
8 |
0.092 |
0.014 |
0.008 |
10.204 |
| Metro |
10 |
0.364 |
0.008 |
0.004 |
93.520 |
| Metro |
12 |
0.597 |
0.011 |
0.008 |
71.702 |
| Metro |
15 |
0.628 |
0.011 |
0.005 |
127.493 |
| Metro |
18 |
0.620 |
0.011 |
0.010 |
58.307 |
| DEMetro_Z |
5 |
0.030 |
0.016 |
0.006 |
2.425 |
| DEMetro_Z |
8 |
0.127 |
0.014 |
0.008 |
14.750 |
| DEMetro_Z |
10 |
0.427 |
0.008 |
0.004 |
109.951 |
| DEMetro_Z |
12 |
0.428 |
0.011 |
0.008 |
51.048 |
| DEMetro_Z |
15 |
0.523 |
0.011 |
0.005 |
105.803 |
| DEMetro_Z |
18 |
0.613 |
0.011 |
0.010 |
57.632 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
Mode Transitions
Mode Transitions (scatter)
KDE + Init Plots
Forest & Ridge Plots
Pooled
Chain
Pairwise Scatter Plots
Pooled
Chain
Vary_Correlation_with_high_Dimension
(MvNormal,
correlation,
12 runs)
Pooled Chains results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
-5.228 |
0.00012 |
-1.620 |
| HMC |
0.3 |
1.006 |
0.333 |
0.972 |
| HMC |
0.5 |
1.986 |
0.0694 |
2.235 |
| HMC |
0.9 |
2.926 |
0.012 |
3.060 |
| HMC |
0.99 |
4.199 |
0.00137 |
8.610 |
| SMC |
0.0 |
-0.559 |
0.582 |
-0.209 |
| SMC |
0.3 |
-0.744 |
0.465 |
-0.347 |
| SMC |
0.5 |
0.193 |
0.849 |
0.078 |
| SMC |
0.9 |
0.039 |
0.97 |
0.016 |
| SMC |
0.99 |
0.001 |
0.999 |
0.000 |
| Metro |
0.0 |
10.457 |
5.83e-10 |
4.479 |
| Metro |
0.3 |
4.216 |
0.00141 |
15.173 |
| Metro |
0.5 |
4.761 |
0.000558 |
13.806 |
| Metro |
0.9 |
3.332 |
0.00665 |
21.488 |
| Metro |
0.99 |
3.321 |
0.00681 |
62.140 |
| DEMetro_Z |
0.0 |
23.966 |
7.61e-11 |
1952.023 |
| DEMetro_Z |
0.3 |
20.692 |
3.71e-10 |
1893.763 |
| DEMetro_Z |
0.5 |
24.301 |
6.54e-11 |
1030.809 |
| DEMetro_Z |
0.9 |
31.303 |
4.14e-12 |
497.796 |
| DEMetro_Z |
0.99 |
29.479 |
8e-12 |
589.174 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0.0
|
-23.985
|
7.55e-11
|
-6.924
|
| HMC_vs_DEMetro_Z |
0.3
|
-20.748
|
3.6e-10
|
-5.990
|
| HMC_vs_DEMetro_Z |
0.5
|
-24.020
|
7.43e-11
|
-6.934
|
| HMC_vs_DEMetro_Z |
0.9
|
-30.915
|
4.81e-12
|
-8.924
|
| HMC_vs_DEMetro_Z |
0.99
|
-28.421
|
1.2e-11
|
-8.204
|
| Metro_vs_SMC |
0.0
|
13.130
|
4.59e-08
|
3.790
|
| Metro_vs_SMC |
0.3
|
4.312
|
0.00123
|
1.245
|
| Metro_vs_SMC |
0.5
|
4.948
|
0.000437
|
1.428
|
| Metro_vs_SMC |
0.9
|
3.394
|
0.00599
|
0.980
|
| Metro_vs_SMC |
0.99
|
3.329
|
0.00672
|
0.961
|
| Metro_vs_DEMetro_Z |
0.0
|
-23.903
|
7.83e-11
|
-6.900
|
| Metro_vs_DEMetro_Z |
0.3
|
-20.427
|
4.26e-10
|
-5.897
|
| Metro_vs_DEMetro_Z |
0.5
|
-24.230
|
6.77e-11
|
-6.995
|
| Metro_vs_DEMetro_Z |
0.9
|
-28.265
|
1.27e-11
|
-8.160
|
| Metro_vs_DEMetro_Z |
0.99
|
-20.714
|
3.67e-10
|
-5.980
|
| HMC_vs_Metro |
0.0
|
-20.971
|
3.21e-10
|
-6.054
|
| HMC_vs_Metro |
0.3
|
-4.470
|
0.000947
|
-1.290
|
| HMC_vs_Metro |
0.5
|
-3.714
|
0.00342
|
-1.072
|
| HMC_vs_Metro |
0.9
|
-2.956
|
0.0131
|
-0.853
|
| HMC_vs_Metro |
0.99
|
-2.806
|
0.0171
|
-0.810
|
| HMC_vs_SMC |
0.0
|
-5.690
|
0.00014
|
-1.642
|
| HMC_vs_SMC |
0.3
|
1.633
|
0.131
|
0.471
|
| HMC_vs_SMC |
0.5
|
2.069
|
0.0629
|
0.597
|
| HMC_vs_SMC |
0.9
|
2.722
|
0.0199
|
0.786
|
| HMC_vs_SMC |
0.99
|
4.306
|
0.00124
|
1.243
|
| DEMetro_Z_vs_SMC |
0.0
|
23.960
|
7.64e-11
|
6.917
|
| DEMetro_Z_vs_SMC |
0.3
|
20.738
|
3.62e-10
|
5.987
|
| DEMetro_Z_vs_SMC |
0.5
|
24.273
|
6.64e-11
|
7.007
|
| DEMetro_Z_vs_SMC |
0.9
|
31.201
|
4.35e-12
|
9.007
|
| DEMetro_Z_vs_SMC |
0.99
|
29.564
|
7.82e-12
|
8.535
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.018 |
0.023 |
0.003 |
-1.620 |
| HMC |
0.3 |
0.025 |
0.021 |
0.004 |
0.972 |
| HMC |
0.5 |
0.036 |
0.021 |
0.007 |
2.235 |
| HMC |
0.9 |
0.065 |
0.021 |
0.014 |
3.060 |
| HMC |
0.99 |
0.107 |
0.015 |
0.011 |
8.610 |
| SMC |
0.0 |
0.022 |
0.023 |
0.003 |
-0.209 |
| SMC |
0.3 |
0.020 |
0.021 |
0.004 |
-0.347 |
| SMC |
0.5 |
0.021 |
0.021 |
0.007 |
0.078 |
| SMC |
0.9 |
0.021 |
0.021 |
0.014 |
0.016 |
| SMC |
0.99 |
0.015 |
0.015 |
0.011 |
0.000 |
| Metro |
0.0 |
0.039 |
0.023 |
0.003 |
4.479 |
| Metro |
0.3 |
0.077 |
0.021 |
0.004 |
15.173 |
| Metro |
0.5 |
0.117 |
0.021 |
0.007 |
13.806 |
| Metro |
0.9 |
0.331 |
0.021 |
0.014 |
21.488 |
| Metro |
0.99 |
0.681 |
0.015 |
0.011 |
62.140 |
| DEMetro_Z |
0.0 |
6.786 |
0.023 |
0.003 |
1952.023 |
| DEMetro_Z |
0.3 |
7.006 |
0.021 |
0.004 |
1893.763 |
| DEMetro_Z |
0.5 |
7.224 |
0.021 |
0.007 |
1030.809 |
| DEMetro_Z |
0.9 |
7.210 |
0.021 |
0.014 |
497.796 |
| DEMetro_Z |
0.99 |
6.336 |
0.015 |
0.011 |
589.174 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
6.301 |
2.5e-06 |
2.679 |
| HMC |
0.3 |
2.379 |
0.0269 |
1.104 |
| HMC |
0.5 |
2.972 |
0.00705 |
1.254 |
| HMC |
0.9 |
3.443 |
0.00451 |
3.711 |
| HMC |
0.99 |
3.507 |
0.00484 |
14.737 |
| SMC |
0.0 |
2.679 |
0.0137 |
1.130 |
| SMC |
0.3 |
1.237 |
0.232 |
0.663 |
| SMC |
0.5 |
1.423 |
0.169 |
0.592 |
| SMC |
0.9 |
-1.521 |
0.146 |
-0.504 |
| SMC |
0.99 |
2.284 |
0.038 |
1.779 |
| Metro |
0.0 |
9.320 |
4.34e-09 |
3.733 |
| Metro |
0.3 |
8.289 |
9.18e-07 |
6.882 |
| Metro |
0.5 |
3.669 |
0.00341 |
6.774 |
| Metro |
0.9 |
5.017 |
0.00038 |
19.851 |
| Metro |
0.99 |
2.437 |
0.033 |
175.933 |
| DEMetro_Z |
0.0 |
21.266 |
2.76e-10 |
36419.860 |
| DEMetro_Z |
0.3 |
26.041 |
3.1e-11 |
40573.602 |
| DEMetro_Z |
0.5 |
25.735 |
3.52e-11 |
19423.903 |
| DEMetro_Z |
0.9 |
18.711 |
1.09e-09 |
9802.503 |
| DEMetro_Z |
0.99 |
21.720 |
2.2e-10 |
11664.493 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0.0
|
2.928
|
0.0137
|
0.845
|
| HMC_vs_SMC |
0.3
|
0.801
|
0.44
|
0.231
|
| HMC_vs_SMC |
0.5
|
1.751
|
0.108
|
0.505
|
| HMC_vs_SMC |
0.9
|
3.829
|
0.0028
|
1.105
|
| HMC_vs_SMC |
0.99
|
2.888
|
0.0148
|
0.834
|
| Metro_vs_DEMetro_Z |
0.0
|
-21.263
|
2.77e-10
|
-6.138
|
| Metro_vs_DEMetro_Z |
0.3
|
-26.031
|
3.11e-11
|
-7.515
|
| Metro_vs_DEMetro_Z |
0.5
|
-25.720
|
3.55e-11
|
-7.425
|
| Metro_vs_DEMetro_Z |
0.9
|
-18.636
|
1.14e-09
|
-5.380
|
| Metro_vs_DEMetro_Z |
0.99
|
-21.559
|
2.39e-10
|
-6.223
|
| HMC_vs_Metro |
0.0
|
-2.019
|
0.0686
|
-0.583
|
| HMC_vs_Metro |
0.3
|
-6.396
|
5.11e-05
|
-1.846
|
| HMC_vs_Metro |
0.5
|
-3.059
|
0.0109
|
-0.883
|
| HMC_vs_Metro |
0.9
|
-3.722
|
0.00337
|
-1.075
|
| HMC_vs_Metro |
0.99
|
-2.276
|
0.0438
|
-0.657
|
| HMC_vs_DEMetro_Z |
0.0
|
-21.265
|
2.77e-10
|
-6.139
|
| HMC_vs_DEMetro_Z |
0.3
|
-26.038
|
3.1e-11
|
-7.517
|
| HMC_vs_DEMetro_Z |
0.5
|
-25.736
|
3.52e-11
|
-7.429
|
| HMC_vs_DEMetro_Z |
0.9
|
-18.711
|
1.09e-09
|
-5.401
|
| HMC_vs_DEMetro_Z |
0.99
|
-21.679
|
2.25e-10
|
-6.258
|
| Metro_vs_SMC |
0.0
|
6.009
|
8.81e-05
|
1.735
|
| Metro_vs_SMC |
0.3
|
6.888
|
2.63e-05
|
1.988
|
| Metro_vs_SMC |
0.5
|
3.753
|
0.00319
|
1.083
|
| Metro_vs_SMC |
0.9
|
5.260
|
0.000269
|
1.518
|
| Metro_vs_SMC |
0.99
|
2.402
|
0.0351
|
0.693
|
| DEMetro_Z_vs_SMC |
0.0
|
21.265
|
2.77e-10
|
6.139
|
| DEMetro_Z_vs_SMC |
0.3
|
26.038
|
3.1e-11
|
7.516
|
| DEMetro_Z_vs_SMC |
0.5
|
25.738
|
3.52e-11
|
7.430
|
| DEMetro_Z_vs_SMC |
0.9
|
18.711
|
1.09e-09
|
5.401
|
| DEMetro_Z_vs_SMC |
0.99
|
21.721
|
2.2e-10
|
6.270
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.045 |
0.033 |
0.005 |
2.679 |
| HMC |
0.3 |
0.036 |
0.031 |
0.004 |
1.104 |
| HMC |
0.5 |
0.044 |
0.032 |
0.010 |
1.254 |
| HMC |
0.9 |
0.097 |
0.031 |
0.018 |
3.711 |
| HMC |
0.99 |
0.204 |
0.021 |
0.012 |
14.737 |
| SMC |
0.0 |
0.038 |
0.033 |
0.005 |
1.130 |
| SMC |
0.3 |
0.034 |
0.031 |
0.004 |
0.663 |
| SMC |
0.5 |
0.038 |
0.032 |
0.010 |
0.592 |
| SMC |
0.9 |
0.022 |
0.031 |
0.018 |
-0.504 |
| SMC |
0.99 |
0.043 |
0.021 |
0.012 |
1.779 |
| Metro |
0.0 |
0.050 |
0.033 |
0.005 |
3.733 |
| Metro |
0.3 |
0.061 |
0.031 |
0.004 |
6.882 |
| Metro |
0.5 |
0.099 |
0.032 |
0.010 |
6.774 |
| Metro |
0.9 |
0.381 |
0.031 |
0.018 |
19.851 |
| Metro |
0.99 |
2.205 |
0.021 |
0.012 |
175.933 |
| DEMetro_Z |
0.0 |
165.856 |
0.033 |
0.005 |
36419.860 |
| DEMetro_Z |
0.3 |
179.445 |
0.031 |
0.004 |
40573.602 |
| DEMetro_Z |
0.5 |
191.966 |
0.032 |
0.010 |
19423.903 |
| DEMetro_Z |
0.9 |
172.546 |
0.031 |
0.018 |
9802.503 |
| DEMetro_Z |
0.99 |
144.847 |
0.021 |
0.012 |
11664.493 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
-1.765 |
0.0959 |
-0.575 |
| HMC |
0.3 |
1.901 |
0.0808 |
2.250 |
| HMC |
0.5 |
2.321 |
0.039 |
3.468 |
| HMC |
0.9 |
5.224 |
0.00014 |
4.580 |
| HMC |
0.99 |
6.074 |
6.96e-05 |
13.519 |
| SMC |
0.0 |
0.098 |
0.922 |
0.038 |
| SMC |
0.3 |
0.373 |
0.714 |
0.194 |
| SMC |
0.5 |
0.752 |
0.46 |
0.329 |
| SMC |
0.9 |
-0.307 |
0.762 |
-0.117 |
| SMC |
0.99 |
0.922 |
0.367 |
0.382 |
| Metro |
0.0 |
12.421 |
6.99e-11 |
6.101 |
| Metro |
0.3 |
4.683 |
0.000658 |
25.018 |
| Metro |
0.5 |
4.992 |
0.000397 |
21.603 |
| Metro |
0.9 |
4.645 |
0.000704 |
32.170 |
| Metro |
0.99 |
4.365 |
0.00113 |
113.701 |
| DEMetro_Z |
0.0 |
64.225 |
1.61e-15 |
5131.237 |
| DEMetro_Z |
0.3 |
49.829 |
2.61e-14 |
6147.386 |
| DEMetro_Z |
0.5 |
55.515 |
7.98e-15 |
3054.682 |
| DEMetro_Z |
0.9 |
53.448 |
1.2e-14 |
1091.043 |
| DEMetro_Z |
0.99 |
52.128 |
1.58e-14 |
1302.226 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0.0
|
-64.061
|
1.66e-15
|
-18.493
|
| Metro_vs_DEMetro_Z |
0.3
|
-49.880
|
2.58e-14
|
-14.399
|
| Metro_vs_DEMetro_Z |
0.5
|
-52.997
|
1.33e-14
|
-15.299
|
| Metro_vs_DEMetro_Z |
0.9
|
-46.393
|
5.71e-14
|
-13.392
|
| Metro_vs_DEMetro_Z |
0.99
|
-34.504
|
1.45e-12
|
-9.960
|
| DEMetro_Z_vs_SMC |
0.0
|
64.259
|
1.61e-15
|
18.550
|
| DEMetro_Z_vs_SMC |
0.3
|
49.875
|
2.59e-14
|
14.398
|
| DEMetro_Z_vs_SMC |
0.5
|
55.529
|
7.97e-15
|
16.030
|
| DEMetro_Z_vs_SMC |
0.9
|
53.472
|
1.21e-14
|
15.436
|
| DEMetro_Z_vs_SMC |
0.99
|
52.202
|
1.57e-14
|
15.070
|
| HMC_vs_DEMetro_Z |
0.0
|
-64.243
|
1.61e-15
|
-18.545
|
| HMC_vs_DEMetro_Z |
0.3
|
-49.882
|
2.58e-14
|
-14.400
|
| HMC_vs_DEMetro_Z |
0.5
|
-55.592
|
7.87e-15
|
-16.048
|
| HMC_vs_DEMetro_Z |
0.9
|
-52.366
|
1.52e-14
|
-15.117
|
| HMC_vs_DEMetro_Z |
0.99
|
-51.051
|
2e-14
|
-14.737
|
| HMC_vs_Metro |
0.0
|
-18.314
|
1.37e-09
|
-5.287
|
| HMC_vs_Metro |
0.3
|
-4.673
|
0.00068
|
-1.349
|
| HMC_vs_Metro |
0.5
|
-3.916
|
0.00241
|
-1.130
|
| HMC_vs_Metro |
0.9
|
-4.063
|
0.00187
|
-1.173
|
| HMC_vs_Metro |
0.99
|
-3.920
|
0.00239
|
-1.132
|
| HMC_vs_SMC |
0.0
|
-2.232
|
0.0474
|
-0.644
|
| HMC_vs_SMC |
0.3
|
1.907
|
0.0829
|
0.551
|
| HMC_vs_SMC |
0.5
|
2.234
|
0.0472
|
0.645
|
| HMC_vs_SMC |
0.9
|
5.350
|
0.000234
|
1.544
|
| HMC_vs_SMC |
0.99
|
5.889
|
0.000105
|
1.700
|
| Metro_vs_SMC |
0.0
|
14.097
|
2.19e-08
|
4.070
|
| Metro_vs_SMC |
0.3
|
4.551
|
0.000828
|
1.314
|
| Metro_vs_SMC |
0.5
|
5.060
|
0.000367
|
1.461
|
| Metro_vs_SMC |
0.9
|
4.748
|
0.000602
|
1.371
|
| Metro_vs_SMC |
0.99
|
4.336
|
0.00118
|
1.252
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.028 |
0.029 |
0.002 |
-0.575 |
| HMC |
0.3 |
0.031 |
0.028 |
0.002 |
2.250 |
| HMC |
0.5 |
0.039 |
0.027 |
0.004 |
3.468 |
| HMC |
0.9 |
0.072 |
0.027 |
0.010 |
4.580 |
| HMC |
0.99 |
0.120 |
0.021 |
0.007 |
13.519 |
| SMC |
0.0 |
0.029 |
0.029 |
0.002 |
0.038 |
| SMC |
0.3 |
0.028 |
0.028 |
0.002 |
0.194 |
| SMC |
0.5 |
0.028 |
0.027 |
0.004 |
0.329 |
| SMC |
0.9 |
0.026 |
0.027 |
0.010 |
-0.117 |
| SMC |
0.99 |
0.024 |
0.021 |
0.007 |
0.382 |
| Metro |
0.0 |
0.041 |
0.029 |
0.002 |
6.101 |
| Metro |
0.3 |
0.070 |
0.028 |
0.002 |
25.018 |
| Metro |
0.5 |
0.106 |
0.027 |
0.004 |
21.603 |
| Metro |
0.9 |
0.342 |
0.027 |
0.010 |
32.170 |
| Metro |
0.99 |
0.851 |
0.021 |
0.007 |
113.701 |
| DEMetro_Z |
0.0 |
10.138 |
0.029 |
0.002 |
5131.237 |
| DEMetro_Z |
0.3 |
10.538 |
0.028 |
0.002 |
6147.386 |
| DEMetro_Z |
0.5 |
11.226 |
0.027 |
0.004 |
3054.682 |
| DEMetro_Z |
0.9 |
10.723 |
0.027 |
0.010 |
1091.043 |
| DEMetro_Z |
0.99 |
9.530 |
0.021 |
0.007 |
1302.226 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
-3.554 |
0.00248 |
-1.163 |
| HMC |
0.3 |
1.483 |
0.163 |
1.650 |
| HMC |
0.5 |
2.303 |
0.0384 |
2.299 |
| HMC |
0.9 |
5.594 |
5.76e-05 |
4.294 |
| HMC |
0.99 |
5.344 |
0.000206 |
10.975 |
| SMC |
0.0 |
-0.583 |
0.566 |
-0.241 |
| SMC |
0.3 |
-0.676 |
0.507 |
-0.339 |
| SMC |
0.5 |
0.683 |
0.502 |
0.276 |
| SMC |
0.9 |
-0.183 |
0.857 |
-0.073 |
| SMC |
0.99 |
1.171 |
0.255 |
0.445 |
| Metro |
0.0 |
9.553 |
2.53e-08 |
5.621 |
| Metro |
0.3 |
4.688 |
0.000648 |
20.933 |
| Metro |
0.5 |
5.265 |
0.00025 |
15.608 |
| Metro |
0.9 |
6.820 |
2.76e-05 |
30.523 |
| Metro |
0.99 |
6.953 |
2.39e-05 |
60.370 |
| DEMetro_Z |
0.0 |
57.856 |
4.56e-15 |
371.137 |
| DEMetro_Z |
0.3 |
54.863 |
8.45e-15 |
419.725 |
| DEMetro_Z |
0.5 |
41.859 |
1.4e-13 |
170.303 |
| DEMetro_Z |
0.9 |
94.669 |
8.48e-21 |
80.900 |
| DEMetro_Z |
0.99 |
55.494 |
1.82e-15 |
95.908 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0.0
|
57.608
|
5.33e-15
|
16.630
|
| DEMetro_Z_vs_SMC |
0.3
|
56.149
|
7.06e-15
|
16.209
|
| DEMetro_Z_vs_SMC |
0.5
|
42.356
|
1.55e-13
|
12.227
|
| DEMetro_Z_vs_SMC |
0.9
|
93.273
|
2.68e-17
|
26.926
|
| DEMetro_Z_vs_SMC |
0.99
|
58.645
|
4.38e-15
|
16.929
|
| HMC_vs_Metro |
0.0
|
-13.651
|
3.06e-08
|
-3.941
|
| HMC_vs_Metro |
0.3
|
-4.907
|
0.000467
|
-1.416
|
| HMC_vs_Metro |
0.5
|
-4.221
|
0.00143
|
-1.219
|
| HMC_vs_Metro |
0.9
|
-6.012
|
8.77e-05
|
-1.736
|
| HMC_vs_Metro |
0.99
|
-5.616
|
0.000157
|
-1.621
|
| Metro_vs_DEMetro_Z |
0.0
|
-57.570
|
5.37e-15
|
-16.619
|
| Metro_vs_DEMetro_Z |
0.3
|
-42.624
|
1.44e-13
|
-12.304
|
| Metro_vs_DEMetro_Z |
0.5
|
-37.113
|
6.56e-13
|
-10.714
|
| Metro_vs_DEMetro_Z |
0.9
|
-11.941
|
1.22e-07
|
-3.447
|
| Metro_vs_DEMetro_Z |
0.99
|
-4.205
|
0.00147
|
-1.214
|
| HMC_vs_SMC |
0.0
|
-2.668
|
0.0219
|
-0.770
|
| HMC_vs_SMC |
0.3
|
1.966
|
0.075
|
0.568
|
| HMC_vs_SMC |
0.5
|
2.157
|
0.054
|
0.623
|
| HMC_vs_SMC |
0.9
|
6.123
|
7.49e-05
|
1.767
|
| HMC_vs_SMC |
0.99
|
5.122
|
0.000332
|
1.479
|
| Metro_vs_SMC |
0.0
|
10.139
|
6.44e-07
|
2.927
|
| Metro_vs_SMC |
0.3
|
4.662
|
0.000692
|
1.346
|
| Metro_vs_SMC |
0.5
|
5.269
|
0.000265
|
1.521
|
| Metro_vs_SMC |
0.9
|
7.010
|
2.24e-05
|
2.023
|
| Metro_vs_SMC |
0.99
|
6.843
|
2.79e-05
|
1.976
|
| HMC_vs_DEMetro_Z |
0.0
|
-58.133
|
4.82e-15
|
-16.782
|
| HMC_vs_DEMetro_Z |
0.3
|
-55.472
|
8.06e-15
|
-16.013
|
| HMC_vs_DEMetro_Z |
0.5
|
-39.117
|
3.69e-13
|
-11.292
|
| HMC_vs_DEMetro_Z |
0.9
|
-61.519
|
2.59e-15
|
-17.759
|
| HMC_vs_DEMetro_Z |
0.99
|
-36.206
|
8.59e-13
|
-10.452
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.013 |
0.015 |
0.002 |
-1.163 |
| HMC |
0.3 |
0.017 |
0.014 |
0.001 |
1.650 |
| HMC |
0.5 |
0.022 |
0.014 |
0.003 |
2.299 |
| HMC |
0.9 |
0.045 |
0.015 |
0.007 |
4.294 |
| HMC |
0.99 |
0.078 |
0.012 |
0.006 |
10.975 |
| SMC |
0.0 |
0.014 |
0.015 |
0.002 |
-0.241 |
| SMC |
0.3 |
0.014 |
0.014 |
0.001 |
-0.339 |
| SMC |
0.5 |
0.015 |
0.014 |
0.003 |
0.276 |
| SMC |
0.9 |
0.015 |
0.015 |
0.007 |
-0.073 |
| SMC |
0.99 |
0.015 |
0.012 |
0.006 |
0.445 |
| Metro |
0.0 |
0.023 |
0.015 |
0.002 |
5.621 |
| Metro |
0.3 |
0.043 |
0.014 |
0.001 |
20.933 |
| Metro |
0.5 |
0.067 |
0.014 |
0.003 |
15.608 |
| Metro |
0.9 |
0.227 |
0.015 |
0.007 |
30.523 |
| Metro |
0.99 |
0.376 |
0.012 |
0.006 |
60.370 |
| DEMetro_Z |
0.0 |
0.580 |
0.015 |
0.002 |
371.137 |
| DEMetro_Z |
0.3 |
0.583 |
0.014 |
0.001 |
419.725 |
| DEMetro_Z |
0.5 |
0.585 |
0.014 |
0.003 |
170.303 |
| DEMetro_Z |
0.9 |
0.575 |
0.015 |
0.007 |
80.900 |
| DEMetro_Z |
0.99 |
0.590 |
0.012 |
0.006 |
95.908 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
R Hat (scatter)
Mode Transitions
One Chain results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
-3.333 |
0.00341 |
-1.165 |
| HMC |
0.3 |
0.612 |
0.552 |
0.668 |
| HMC |
0.5 |
2.692 |
0.017 |
2.031 |
| HMC |
0.9 |
2.995 |
0.0103 |
2.942 |
| HMC |
0.99 |
3.387 |
0.00595 |
11.535 |
| SMC |
0.0 |
-0.828 |
0.416 |
-0.360 |
| SMC |
0.3 |
-0.184 |
0.856 |
-0.132 |
| SMC |
0.5 |
-1.384 |
0.183 |
-0.466 |
| SMC |
0.9 |
-0.181 |
0.858 |
-0.066 |
| SMC |
0.99 |
0.836 |
0.413 |
0.417 |
| Metro |
0.0 |
10.529 |
8.6e-10 |
3.862 |
| Metro |
0.3 |
4.283 |
0.00124 |
12.440 |
| Metro |
0.5 |
4.054 |
0.00187 |
17.440 |
| Metro |
0.9 |
4.483 |
0.000914 |
23.650 |
| Metro |
0.99 |
6.242 |
6.33e-05 |
185.089 |
| DEMetro_Z |
0.0 |
12.792 |
6.01e-08 |
3091.522 |
| DEMetro_Z |
0.3 |
17.701 |
1.97e-09 |
3389.717 |
| DEMetro_Z |
0.5 |
29.622 |
7.64e-12 |
1784.172 |
| DEMetro_Z |
0.9 |
27.867 |
1.48e-11 |
779.199 |
| DEMetro_Z |
0.99 |
20.930 |
3.28e-10 |
955.487 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0.0
|
-12.799
|
5.98e-08
|
-3.695
|
| HMC_vs_DEMetro_Z |
0.3
|
-17.705
|
1.97e-09
|
-5.111
|
| HMC_vs_DEMetro_Z |
0.5
|
-29.657
|
7.55e-12
|
-8.561
|
| HMC_vs_DEMetro_Z |
0.9
|
-27.514
|
1.71e-11
|
-7.943
|
| HMC_vs_DEMetro_Z |
0.99
|
-20.599
|
3.89e-10
|
-5.946
|
| Metro_vs_SMC |
0.0
|
12.326
|
8.83e-08
|
3.558
|
| Metro_vs_SMC |
0.3
|
4.653
|
0.000702
|
1.343
|
| Metro_vs_SMC |
0.5
|
4.127
|
0.00168
|
1.191
|
| Metro_vs_SMC |
0.9
|
4.502
|
0.000898
|
1.300
|
| Metro_vs_SMC |
0.99
|
6.265
|
6.13e-05
|
1.809
|
| Metro_vs_DEMetro_Z |
0.0
|
-12.774
|
6.1e-08
|
-3.688
|
| Metro_vs_DEMetro_Z |
0.3
|
-17.576
|
2.13e-09
|
-5.074
|
| Metro_vs_DEMetro_Z |
0.5
|
-29.206
|
8.93e-12
|
-8.431
|
| Metro_vs_DEMetro_Z |
0.9
|
-26.815
|
2.26e-11
|
-7.741
|
| Metro_vs_DEMetro_Z |
0.99
|
-17.293
|
2.53e-09
|
-4.992
|
| HMC_vs_Metro |
0.0
|
-15.747
|
6.83e-09
|
-4.546
|
| HMC_vs_Metro |
0.3
|
-3.778
|
0.00306
|
-1.091
|
| HMC_vs_Metro |
0.5
|
-3.357
|
0.0064
|
-0.969
|
| HMC_vs_Metro |
0.9
|
-3.992
|
0.00211
|
-1.152
|
| HMC_vs_Metro |
0.99
|
-5.977
|
9.22e-05
|
-1.726
|
| HMC_vs_SMC |
0.0
|
-2.993
|
0.0122
|
-0.864
|
| HMC_vs_SMC |
0.3
|
0.670
|
0.516
|
0.194
|
| HMC_vs_SMC |
0.5
|
3.246
|
0.00779
|
0.937
|
| HMC_vs_SMC |
0.9
|
3.232
|
0.00799
|
0.933
|
| HMC_vs_SMC |
0.99
|
3.212
|
0.00828
|
0.927
|
| DEMetro_Z_vs_SMC |
0.0
|
12.792
|
6.01e-08
|
3.693
|
| DEMetro_Z_vs_SMC |
0.3
|
17.704
|
1.97e-09
|
5.111
|
| DEMetro_Z_vs_SMC |
0.5
|
29.605
|
7.7e-12
|
8.546
|
| DEMetro_Z_vs_SMC |
0.9
|
27.970
|
1.43e-11
|
8.074
|
| DEMetro_Z_vs_SMC |
0.99
|
21.056
|
3.08e-10
|
6.078
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.019 |
0.023 |
0.003 |
-1.165 |
| HMC |
0.3 |
0.024 |
0.021 |
0.004 |
0.668 |
| HMC |
0.5 |
0.035 |
0.021 |
0.007 |
2.031 |
| HMC |
0.9 |
0.064 |
0.021 |
0.014 |
2.942 |
| HMC |
0.99 |
0.138 |
0.015 |
0.011 |
11.535 |
| SMC |
0.0 |
0.022 |
0.023 |
0.003 |
-0.360 |
| SMC |
0.3 |
0.021 |
0.021 |
0.004 |
-0.132 |
| SMC |
0.5 |
0.017 |
0.021 |
0.007 |
-0.466 |
| SMC |
0.9 |
0.020 |
0.021 |
0.014 |
-0.066 |
| SMC |
0.99 |
0.019 |
0.015 |
0.011 |
0.417 |
| Metro |
0.0 |
0.037 |
0.023 |
0.003 |
3.862 |
| Metro |
0.3 |
0.067 |
0.021 |
0.004 |
12.440 |
| Metro |
0.5 |
0.143 |
0.021 |
0.007 |
17.440 |
| Metro |
0.9 |
0.363 |
0.021 |
0.014 |
23.650 |
| Metro |
0.99 |
2.000 |
0.015 |
0.011 |
185.089 |
| DEMetro_Z |
0.0 |
10.734 |
0.023 |
0.003 |
3091.522 |
| DEMetro_Z |
0.3 |
12.523 |
0.021 |
0.004 |
3389.717 |
| DEMetro_Z |
0.5 |
12.488 |
0.021 |
0.007 |
1784.172 |
| DEMetro_Z |
0.9 |
11.274 |
0.021 |
0.014 |
779.199 |
| DEMetro_Z |
0.99 |
10.266 |
0.015 |
0.011 |
955.487 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
4.967 |
6.52e-05 |
2.302 |
| HMC |
0.3 |
4.081 |
0.000495 |
1.696 |
| HMC |
0.5 |
1.134 |
0.269 |
0.431 |
| HMC |
0.9 |
2.289 |
0.0419 |
4.509 |
| HMC |
0.99 |
2.785 |
0.0177 |
20.057 |
| SMC |
0.0 |
-0.134 |
0.895 |
-0.049 |
| SMC |
0.3 |
2.216 |
0.0376 |
0.852 |
| SMC |
0.5 |
0.375 |
0.712 |
0.128 |
| SMC |
0.9 |
-1.925 |
0.0714 |
-0.630 |
| SMC |
0.99 |
1.668 |
0.112 |
0.868 |
| Metro |
0.0 |
7.973 |
2.75e-07 |
4.532 |
| Metro |
0.3 |
9.261 |
8.55e-08 |
6.156 |
| Metro |
0.5 |
4.636 |
0.000539 |
5.678 |
| Metro |
0.9 |
8.093 |
4.92e-06 |
20.090 |
| Metro |
0.99 |
16.010 |
5.03e-09 |
64.671 |
| DEMetro_Z |
0.0 |
9.710 |
9.92e-07 |
4452.183 |
| DEMetro_Z |
0.3 |
11.326 |
2.1e-07 |
4643.030 |
| DEMetro_Z |
0.5 |
6.479 |
4.56e-05 |
1500.108 |
| DEMetro_Z |
0.9 |
8.628 |
3.16e-06 |
1149.339 |
| DEMetro_Z |
0.99 |
8.589 |
3.3e-06 |
1748.721 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0.0
|
6.486
|
4.52e-05
|
1.872
|
| HMC_vs_SMC |
0.3
|
2.099
|
0.0597
|
0.606
|
| HMC_vs_SMC |
0.5
|
1.143
|
0.277
|
0.330
|
| HMC_vs_SMC |
0.9
|
2.570
|
0.0261
|
0.742
|
| HMC_vs_SMC |
0.99
|
2.691
|
0.021
|
0.777
|
| Metro_vs_DEMetro_Z |
0.0
|
-9.700
|
1e-06
|
-2.800
|
| Metro_vs_DEMetro_Z |
0.3
|
-11.308
|
2.14e-07
|
-3.264
|
| Metro_vs_DEMetro_Z |
0.5
|
-6.450
|
4.74e-05
|
-1.862
|
| Metro_vs_DEMetro_Z |
0.9
|
-8.594
|
3.29e-06
|
-2.481
|
| Metro_vs_DEMetro_Z |
0.99
|
-8.257
|
4.83e-06
|
-2.383
|
| HMC_vs_Metro |
0.0
|
-3.261
|
0.00759
|
-0.941
|
| HMC_vs_Metro |
0.3
|
-6.543
|
4.18e-05
|
-1.889
|
| HMC_vs_Metro |
0.5
|
-4.430
|
0.00101
|
-1.279
|
| HMC_vs_Metro |
0.9
|
-4.556
|
0.000822
|
-1.315
|
| HMC_vs_Metro |
0.99
|
-4.611
|
0.000751
|
-1.331
|
| HMC_vs_DEMetro_Z |
0.0
|
-9.705
|
9.97e-07
|
-2.802
|
| HMC_vs_DEMetro_Z |
0.3
|
-11.322
|
2.11e-07
|
-3.268
|
| HMC_vs_DEMetro_Z |
0.5
|
-6.477
|
4.57e-05
|
-1.870
|
| HMC_vs_DEMetro_Z |
0.9
|
-8.570
|
3.37e-06
|
-2.474
|
| HMC_vs_DEMetro_Z |
0.99
|
-8.448
|
3.88e-06
|
-2.439
|
| Metro_vs_SMC |
0.0
|
7.112
|
1.96e-05
|
2.053
|
| Metro_vs_SMC |
0.3
|
6.849
|
2.77e-05
|
1.977
|
| Metro_vs_SMC |
0.5
|
5.182
|
0.000303
|
1.496
|
| Metro_vs_SMC |
0.9
|
8.577
|
3.35e-06
|
2.476
|
| Metro_vs_SMC |
0.99
|
15.349
|
8.95e-09
|
4.431
|
| DEMetro_Z_vs_SMC |
0.0
|
9.707
|
9.94e-07
|
2.802
|
| DEMetro_Z_vs_SMC |
0.3
|
11.324
|
2.11e-07
|
3.269
|
| DEMetro_Z_vs_SMC |
0.5
|
6.478
|
4.57e-05
|
1.870
|
| DEMetro_Z_vs_SMC |
0.9
|
8.641
|
3.12e-06
|
2.494
|
| DEMetro_Z_vs_SMC |
0.99
|
8.580
|
3.34e-06
|
2.477
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.043 |
0.033 |
0.005 |
2.302 |
| HMC |
0.3 |
0.038 |
0.031 |
0.004 |
1.696 |
| HMC |
0.5 |
0.036 |
0.032 |
0.010 |
0.431 |
| HMC |
0.9 |
0.111 |
0.031 |
0.018 |
4.509 |
| HMC |
0.99 |
0.270 |
0.021 |
0.012 |
20.057 |
| SMC |
0.0 |
0.032 |
0.033 |
0.005 |
-0.049 |
| SMC |
0.3 |
0.034 |
0.031 |
0.004 |
0.852 |
| SMC |
0.5 |
0.033 |
0.032 |
0.010 |
0.128 |
| SMC |
0.9 |
0.020 |
0.031 |
0.018 |
-0.630 |
| SMC |
0.99 |
0.032 |
0.021 |
0.012 |
0.868 |
| Metro |
0.0 |
0.053 |
0.033 |
0.005 |
4.532 |
| Metro |
0.3 |
0.058 |
0.031 |
0.004 |
6.156 |
| Metro |
0.5 |
0.088 |
0.032 |
0.010 |
5.678 |
| Metro |
0.9 |
0.385 |
0.031 |
0.018 |
20.090 |
| Metro |
0.99 |
0.824 |
0.021 |
0.012 |
64.671 |
| DEMetro_Z |
0.0 |
20.304 |
0.033 |
0.005 |
4452.183 |
| DEMetro_Z |
0.3 |
20.562 |
0.031 |
0.004 |
4643.030 |
| DEMetro_Z |
0.5 |
14.855 |
0.032 |
0.010 |
1500.108 |
| DEMetro_Z |
0.9 |
20.259 |
0.031 |
0.018 |
1149.339 |
| DEMetro_Z |
0.99 |
21.733 |
0.021 |
0.012 |
1748.721 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
0.232 |
0.819 |
0.079 |
| HMC |
0.3 |
1.565 |
0.144 |
2.126 |
| HMC |
0.5 |
3.329 |
0.00513 |
2.923 |
| HMC |
0.9 |
4.059 |
0.00149 |
4.824 |
| HMC |
0.99 |
4.313 |
0.0012 |
16.696 |
| SMC |
0.0 |
-0.514 |
0.613 |
-0.241 |
| SMC |
0.3 |
0.317 |
0.756 |
0.267 |
| SMC |
0.5 |
-0.700 |
0.493 |
-0.233 |
| SMC |
0.9 |
-0.999 |
0.332 |
-0.328 |
| SMC |
0.99 |
1.473 |
0.155 |
0.622 |
| Metro |
0.0 |
12.263 |
4.73e-11 |
5.642 |
| Metro |
0.3 |
5.052 |
0.000359 |
20.068 |
| Metro |
0.5 |
4.180 |
0.00152 |
25.622 |
| Metro |
0.9 |
5.795 |
0.000117 |
30.546 |
| Metro |
0.99 |
6.713 |
3.32e-05 |
220.610 |
| DEMetro_Z |
0.0 |
13.047 |
4.9e-08 |
4573.180 |
| DEMetro_Z |
0.3 |
17.447 |
2.3e-09 |
6159.739 |
| DEMetro_Z |
0.5 |
28.146 |
1.33e-11 |
2801.409 |
| DEMetro_Z |
0.9 |
32.018 |
3.27e-12 |
948.719 |
| DEMetro_Z |
0.99 |
20.306 |
4.54e-10 |
1194.145 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0.0
|
-13.032
|
4.96e-08
|
-3.762
|
| Metro_vs_DEMetro_Z |
0.3
|
-17.338
|
2.46e-09
|
-5.005
|
| Metro_vs_DEMetro_Z |
0.5
|
-27.535
|
1.69e-11
|
-7.949
|
| Metro_vs_DEMetro_Z |
0.9
|
-30.820
|
4.97e-12
|
-8.897
|
| Metro_vs_DEMetro_Z |
0.99
|
-17.292
|
2.53e-09
|
-4.992
|
| DEMetro_Z_vs_SMC |
0.0
|
13.046
|
4.91e-08
|
3.766
|
| DEMetro_Z_vs_SMC |
0.3
|
17.444
|
2.3e-09
|
5.036
|
| DEMetro_Z_vs_SMC |
0.5
|
28.121
|
1.35e-11
|
8.118
|
| DEMetro_Z_vs_SMC |
0.9
|
32.068
|
3.23e-12
|
9.257
|
| DEMetro_Z_vs_SMC |
0.99
|
20.372
|
4.39e-10
|
5.881
|
| HMC_vs_DEMetro_Z |
0.0
|
-13.048
|
4.9e-08
|
-3.767
|
| HMC_vs_DEMetro_Z |
0.3
|
-17.447
|
2.3e-09
|
-5.036
|
| HMC_vs_DEMetro_Z |
0.5
|
-28.149
|
1.33e-11
|
-8.126
|
| HMC_vs_DEMetro_Z |
0.9
|
-31.589
|
3.8e-12
|
-9.119
|
| HMC_vs_DEMetro_Z |
0.99
|
-20.181
|
4.85e-10
|
-5.826
|
| HMC_vs_Metro |
0.0
|
-13.405
|
3.7e-08
|
-3.870
|
| HMC_vs_Metro |
0.3
|
-4.194
|
0.0015
|
-1.211
|
| HMC_vs_Metro |
0.5
|
-3.520
|
0.0048
|
-1.016
|
| HMC_vs_Metro |
0.9
|
-4.743
|
0.000606
|
-1.369
|
| HMC_vs_Metro |
0.99
|
-6.494
|
4.46e-05
|
-1.875
|
| HMC_vs_SMC |
0.0
|
0.994
|
0.342
|
0.287
|
| HMC_vs_SMC |
0.3
|
1.232
|
0.244
|
0.356
|
| HMC_vs_SMC |
0.5
|
3.521
|
0.00479
|
1.017
|
| HMC_vs_SMC |
0.9
|
4.387
|
0.00109
|
1.266
|
| HMC_vs_SMC |
0.99
|
4.271
|
0.00132
|
1.233
|
| Metro_vs_SMC |
0.0
|
14.758
|
1.35e-08
|
4.260
|
| Metro_vs_SMC |
0.3
|
5.348
|
0.000235
|
1.544
|
| Metro_vs_SMC |
0.5
|
4.217
|
0.00144
|
1.217
|
| Metro_vs_SMC |
0.9
|
5.833
|
0.000114
|
1.684
|
| Metro_vs_SMC |
0.99
|
6.733
|
3.23e-05
|
1.944
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.029 |
0.029 |
0.002 |
0.079 |
| HMC |
0.3 |
0.031 |
0.028 |
0.002 |
2.126 |
| HMC |
0.5 |
0.037 |
0.027 |
0.004 |
2.923 |
| HMC |
0.9 |
0.074 |
0.027 |
0.010 |
4.824 |
| HMC |
0.99 |
0.143 |
0.021 |
0.007 |
16.696 |
| SMC |
0.0 |
0.029 |
0.029 |
0.002 |
-0.241 |
| SMC |
0.3 |
0.028 |
0.028 |
0.002 |
0.267 |
| SMC |
0.5 |
0.026 |
0.027 |
0.004 |
-0.233 |
| SMC |
0.9 |
0.024 |
0.027 |
0.010 |
-0.328 |
| SMC |
0.99 |
0.025 |
0.021 |
0.007 |
0.622 |
| Metro |
0.0 |
0.040 |
0.029 |
0.002 |
5.642 |
| Metro |
0.3 |
0.062 |
0.028 |
0.002 |
20.068 |
| Metro |
0.5 |
0.121 |
0.027 |
0.004 |
25.622 |
| Metro |
0.9 |
0.326 |
0.027 |
0.010 |
30.546 |
| Metro |
0.99 |
1.632 |
0.021 |
0.007 |
220.610 |
| DEMetro_Z |
0.0 |
9.039 |
0.029 |
0.002 |
4573.180 |
| DEMetro_Z |
0.3 |
10.559 |
0.028 |
0.002 |
6159.739 |
| DEMetro_Z |
0.5 |
10.298 |
0.027 |
0.004 |
2801.409 |
| DEMetro_Z |
0.9 |
9.327 |
0.027 |
0.010 |
948.719 |
| DEMetro_Z |
0.99 |
8.741 |
0.021 |
0.007 |
1194.145 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
-1.705 |
0.103 |
-0.641 |
| HMC |
0.3 |
1.228 |
0.243 |
1.598 |
| HMC |
0.5 |
2.646 |
0.0187 |
2.030 |
| HMC |
0.9 |
4.686 |
0.000409 |
4.470 |
| HMC |
0.99 |
4.521 |
0.000829 |
13.242 |
| SMC |
0.0 |
-1.571 |
0.131 |
-0.662 |
| SMC |
0.3 |
-0.086 |
0.932 |
-0.071 |
| SMC |
0.5 |
-0.559 |
0.582 |
-0.196 |
| SMC |
0.9 |
-1.511 |
0.152 |
-0.470 |
| SMC |
0.99 |
1.340 |
0.194 |
0.569 |
| Metro |
0.0 |
11.967 |
4.51e-11 |
5.081 |
| Metro |
0.3 |
5.034 |
0.000365 |
16.815 |
| Metro |
0.5 |
4.153 |
0.00158 |
18.663 |
| Metro |
0.9 |
7.951 |
6.42e-06 |
29.591 |
| Metro |
0.99 |
16.565 |
3.88e-09 |
142.221 |
| DEMetro_Z |
0.0 |
55.457 |
7.79e-15 |
595.479 |
| DEMetro_Z |
0.3 |
38.420 |
4.44e-13 |
686.109 |
| DEMetro_Z |
0.5 |
26.050 |
3.02e-11 |
292.382 |
| DEMetro_Z |
0.9 |
67.878 |
2.65e-16 |
135.498 |
| DEMetro_Z |
0.99 |
55.147 |
4.93e-15 |
154.305 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0.0
|
55.568
|
7.91e-15
|
16.041
|
| DEMetro_Z_vs_SMC |
0.3
|
38.138
|
4.87e-13
|
11.010
|
| DEMetro_Z_vs_SMC |
0.5
|
25.929
|
3.25e-11
|
7.485
|
| DEMetro_Z_vs_SMC |
0.9
|
69.347
|
6.96e-16
|
20.019
|
| DEMetro_Z_vs_SMC |
0.99
|
56.318
|
6.83e-15
|
16.258
|
| HMC_vs_Metro |
0.0
|
-16.765
|
3.51e-09
|
-4.840
|
| HMC_vs_Metro |
0.3
|
-4.150
|
0.00162
|
-1.198
|
| HMC_vs_Metro |
0.5
|
-3.487
|
0.00508
|
-1.007
|
| HMC_vs_Metro |
0.9
|
-6.673
|
3.5e-05
|
-1.926
|
| HMC_vs_Metro |
0.99
|
-15.726
|
6.92e-09
|
-4.540
|
| Metro_vs_DEMetro_Z |
0.0
|
-55.197
|
8.51e-15
|
-15.934
|
| Metro_vs_DEMetro_Z |
0.3
|
-35.362
|
1.11e-12
|
-10.208
|
| Metro_vs_DEMetro_Z |
0.5
|
-22.553
|
1.47e-10
|
-6.510
|
| Metro_vs_DEMetro_Z |
0.9
|
-25.801
|
3.43e-11
|
-7.448
|
| Metro_vs_DEMetro_Z |
0.99
|
-1.300
|
0.22
|
-0.375
|
| HMC_vs_SMC |
0.0
|
0.099
|
0.923
|
0.029
|
| HMC_vs_SMC |
0.3
|
1.146
|
0.276
|
0.331
|
| HMC_vs_SMC |
0.5
|
2.865
|
0.0154
|
0.827
|
| HMC_vs_SMC |
0.9
|
5.325
|
0.000243
|
1.537
|
| HMC_vs_SMC |
0.99
|
4.510
|
0.000887
|
1.302
|
| Metro_vs_SMC |
0.0
|
17.847
|
1.81e-09
|
5.152
|
| Metro_vs_SMC |
0.3
|
5.278
|
0.000261
|
1.524
|
| Metro_vs_SMC |
0.5
|
4.177
|
0.00154
|
1.206
|
| Metro_vs_SMC |
0.9
|
7.988
|
6.63e-06
|
2.306
|
| Metro_vs_SMC |
0.99
|
16.840
|
3.35e-09
|
4.861
|
| HMC_vs_DEMetro_Z |
0.0
|
-55.588
|
7.88e-15
|
-16.047
|
| HMC_vs_DEMetro_Z |
0.3
|
-38.259
|
4.7e-13
|
-11.045
|
| HMC_vs_DEMetro_Z |
0.5
|
-25.928
|
3.25e-11
|
-7.485
|
| HMC_vs_DEMetro_Z |
0.9
|
-61.963
|
2.39e-15
|
-17.887
|
| HMC_vs_DEMetro_Z |
0.99
|
-29.993
|
6.68e-12
|
-8.658
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.014 |
0.015 |
0.002 |
-0.641 |
| HMC |
0.3 |
0.016 |
0.014 |
0.001 |
1.598 |
| HMC |
0.5 |
0.021 |
0.014 |
0.003 |
2.030 |
| HMC |
0.9 |
0.046 |
0.015 |
0.007 |
4.470 |
| HMC |
0.99 |
0.092 |
0.012 |
0.006 |
13.242 |
| SMC |
0.0 |
0.014 |
0.015 |
0.002 |
-0.662 |
| SMC |
0.3 |
0.014 |
0.014 |
0.001 |
-0.071 |
| SMC |
0.5 |
0.014 |
0.014 |
0.003 |
-0.196 |
| SMC |
0.9 |
0.012 |
0.015 |
0.007 |
-0.470 |
| SMC |
0.99 |
0.016 |
0.012 |
0.006 |
0.569 |
| Metro |
0.0 |
0.022 |
0.015 |
0.002 |
5.081 |
| Metro |
0.3 |
0.037 |
0.014 |
0.001 |
16.815 |
| Metro |
0.5 |
0.077 |
0.014 |
0.003 |
18.663 |
| Metro |
0.9 |
0.220 |
0.015 |
0.007 |
29.591 |
| Metro |
0.99 |
0.868 |
0.012 |
0.006 |
142.221 |
| DEMetro_Z |
0.0 |
0.921 |
0.015 |
0.002 |
595.479 |
| DEMetro_Z |
0.3 |
0.945 |
0.014 |
0.001 |
686.109 |
| DEMetro_Z |
0.5 |
0.995 |
0.014 |
0.003 |
292.382 |
| DEMetro_Z |
0.9 |
0.953 |
0.015 |
0.007 |
135.498 |
| DEMetro_Z |
0.99 |
0.941 |
0.012 |
0.006 |
154.305 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
Mode Transitions
Forest & Ridge Plots
Pooled
Chain
Pairwise Scatter Plots
Pooled
Chain
Vary_Correlation_with_heavy_Tails
(MvStudentT,
correlation,
12 runs)
Pooled Chains results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
-1.174 |
0.253 |
-0.476 |
| HMC |
0.3 |
0.234 |
0.817 |
0.106 |
| HMC |
0.5 |
1.349 |
0.191 |
0.554 |
| HMC |
0.9 |
2.626 |
0.021 |
2.645 |
| HMC |
0.99 |
0.608 |
0.551 |
0.205 |
| SMC |
0.0 |
-0.226 |
0.823 |
-0.079 |
| SMC |
0.3 |
-0.765 |
0.453 |
-0.281 |
| SMC |
0.5 |
-0.291 |
0.774 |
-0.106 |
| SMC |
0.9 |
0.965 |
0.348 |
0.574 |
| SMC |
0.99 |
-0.070 |
0.945 |
-0.027 |
| Metro |
0.0 |
1.792 |
0.0886 |
0.907 |
| Metro |
0.3 |
3.263 |
0.00388 |
1.601 |
| Metro |
0.5 |
3.044 |
0.0105 |
4.959 |
| Metro |
0.9 |
2.775 |
0.0175 |
5.611 |
| Metro |
0.99 |
4.358 |
0.000951 |
6.360 |
| DEMetro_Z |
0.0 |
4.120 |
0.000671 |
2.379 |
| DEMetro_Z |
0.3 |
3.073 |
0.00752 |
2.123 |
| DEMetro_Z |
0.5 |
3.486 |
0.00218 |
1.589 |
| DEMetro_Z |
0.9 |
2.208 |
0.0486 |
5.031 |
| DEMetro_Z |
0.99 |
1.412 |
0.174 |
0.721 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0.0
|
-4.716
|
0.000633
|
-1.362
|
| HMC_vs_DEMetro_Z |
0.3
|
-2.394
|
0.0356
|
-0.691
|
| HMC_vs_DEMetro_Z |
0.5
|
-2.937
|
0.0135
|
-0.848
|
| HMC_vs_DEMetro_Z |
0.9
|
-1.471
|
0.169
|
-0.425
|
| HMC_vs_DEMetro_Z |
0.99
|
-1.040
|
0.321
|
-0.300
|
| Metro_vs_SMC |
0.0
|
2.349
|
0.0386
|
0.678
|
| Metro_vs_SMC |
0.3
|
5.325
|
0.000243
|
1.537
|
| Metro_vs_SMC |
0.5
|
3.119
|
0.00976
|
0.900
|
| Metro_vs_SMC |
0.9
|
2.480
|
0.0306
|
0.716
|
| Metro_vs_SMC |
0.99
|
4.235
|
0.0014
|
1.223
|
| Metro_vs_DEMetro_Z |
0.0
|
-2.100
|
0.0596
|
-0.606
|
| Metro_vs_DEMetro_Z |
0.3
|
-0.585
|
0.57
|
-0.169
|
| Metro_vs_DEMetro_Z |
0.5
|
1.981
|
0.0732
|
0.572
|
| Metro_vs_DEMetro_Z |
0.9
|
0.174
|
0.865
|
0.050
|
| Metro_vs_DEMetro_Z |
0.99
|
3.477
|
0.00518
|
1.004
|
| HMC_vs_Metro |
0.0
|
-3.108
|
0.00996
|
-0.897
|
| HMC_vs_Metro |
0.3
|
-2.822
|
0.0166
|
-0.815
|
| HMC_vs_Metro |
0.5
|
-2.639
|
0.0231
|
-0.762
|
| HMC_vs_Metro |
0.9
|
-1.497
|
0.162
|
-0.432
|
| HMC_vs_Metro |
0.99
|
-4.245
|
0.00138
|
-1.225
|
| HMC_vs_SMC |
0.0
|
-1.611
|
0.135
|
-0.465
|
| HMC_vs_SMC |
0.3
|
0.802
|
0.439
|
0.232
|
| HMC_vs_SMC |
0.5
|
1.881
|
0.0866
|
0.543
|
| HMC_vs_SMC |
0.9
|
2.083
|
0.0614
|
0.601
|
| HMC_vs_SMC |
0.99
|
0.666
|
0.519
|
0.192
|
| DEMetro_Z_vs_SMC |
0.0
|
4.950
|
0.000436
|
1.429
|
| DEMetro_Z_vs_SMC |
0.3
|
3.691
|
0.00356
|
1.065
|
| DEMetro_Z_vs_SMC |
0.5
|
4.222
|
0.00143
|
1.219
|
| DEMetro_Z_vs_SMC |
0.9
|
2.067
|
0.0631
|
0.597
|
| DEMetro_Z_vs_SMC |
0.99
|
1.510
|
0.159
|
0.436
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.053 |
0.072 |
0.040 |
-0.476 |
| HMC |
0.3 |
0.061 |
0.058 |
0.035 |
0.106 |
| HMC |
0.5 |
0.075 |
0.054 |
0.037 |
0.554 |
| HMC |
0.9 |
0.121 |
0.046 |
0.028 |
2.645 |
| HMC |
0.99 |
0.088 |
0.070 |
0.087 |
0.205 |
| SMC |
0.0 |
0.069 |
0.072 |
0.040 |
-0.079 |
| SMC |
0.3 |
0.048 |
0.058 |
0.035 |
-0.281 |
| SMC |
0.5 |
0.050 |
0.054 |
0.037 |
-0.106 |
| SMC |
0.9 |
0.062 |
0.046 |
0.028 |
0.574 |
| SMC |
0.99 |
0.068 |
0.070 |
0.087 |
-0.027 |
| Metro |
0.0 |
0.108 |
0.072 |
0.040 |
0.907 |
| Metro |
0.3 |
0.113 |
0.058 |
0.035 |
1.601 |
| Metro |
0.5 |
0.239 |
0.054 |
0.037 |
4.959 |
| Metro |
0.9 |
0.205 |
0.046 |
0.028 |
5.611 |
| Metro |
0.99 |
0.623 |
0.070 |
0.087 |
6.360 |
| DEMetro_Z |
0.0 |
0.167 |
0.072 |
0.040 |
2.379 |
| DEMetro_Z |
0.3 |
0.131 |
0.058 |
0.035 |
2.123 |
| DEMetro_Z |
0.5 |
0.113 |
0.054 |
0.037 |
1.589 |
| DEMetro_Z |
0.9 |
0.189 |
0.046 |
0.028 |
5.031 |
| DEMetro_Z |
0.99 |
0.133 |
0.070 |
0.087 |
0.721 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
-0.169 |
0.867 |
-0.066 |
| HMC |
0.3 |
-1.109 |
0.285 |
-0.348 |
| HMC |
0.5 |
0.798 |
0.435 |
0.446 |
| HMC |
0.9 |
1.673 |
0.117 |
1.421 |
| HMC |
0.99 |
0.800 |
0.433 |
0.286 |
| SMC |
0.0 |
-0.187 |
0.853 |
-0.070 |
| SMC |
0.3 |
-1.649 |
0.124 |
-0.495 |
| SMC |
0.5 |
-0.881 |
0.39 |
-0.295 |
| SMC |
0.9 |
1.200 |
0.248 |
0.826 |
| SMC |
0.99 |
0.852 |
0.408 |
0.671 |
| Metro |
0.0 |
-0.134 |
0.894 |
-0.053 |
| Metro |
0.3 |
-1.447 |
0.171 |
-0.442 |
| Metro |
0.5 |
0.070 |
0.945 |
0.029 |
| Metro |
0.9 |
1.692 |
0.113 |
1.410 |
| Metro |
0.99 |
1.395 |
0.177 |
0.523 |
| DEMetro_Z |
0.0 |
-0.045 |
0.965 |
-0.017 |
| DEMetro_Z |
0.3 |
-0.329 |
0.746 |
-0.112 |
| DEMetro_Z |
0.5 |
0.235 |
0.817 |
0.084 |
| DEMetro_Z |
0.9 |
2.071 |
0.0577 |
1.769 |
| DEMetro_Z |
0.99 |
0.856 |
0.403 |
0.296 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0.0
|
0.092
|
0.929
|
0.026
|
| HMC_vs_SMC |
0.3
|
1.029
|
0.325
|
0.297
|
| HMC_vs_SMC |
0.5
|
1.576
|
0.143
|
0.455
|
| HMC_vs_SMC |
0.9
|
1.494
|
0.163
|
0.431
|
| HMC_vs_SMC |
0.99
|
-0.498
|
0.628
|
-0.144
|
| Metro_vs_DEMetro_Z |
0.0
|
-1.037
|
0.322
|
-0.299
|
| Metro_vs_DEMetro_Z |
0.3
|
-1.653
|
0.127
|
-0.477
|
| Metro_vs_DEMetro_Z |
0.5
|
-0.182
|
0.859
|
-0.053
|
| Metro_vs_DEMetro_Z |
0.9
|
-2.153
|
0.0543
|
-0.622
|
| Metro_vs_DEMetro_Z |
0.99
|
1.046
|
0.318
|
0.302
|
| HMC_vs_Metro |
0.0
|
-0.713
|
0.491
|
-0.206
|
| HMC_vs_Metro |
0.3
|
0.805
|
0.438
|
0.232
|
| HMC_vs_Metro |
0.5
|
0.653
|
0.527
|
0.188
|
| HMC_vs_Metro |
0.9
|
0.028
|
0.978
|
0.008
|
| HMC_vs_Metro |
0.99
|
-0.832
|
0.423
|
-0.240
|
| HMC_vs_DEMetro_Z |
0.0
|
-1.288
|
0.224
|
-0.372
|
| HMC_vs_DEMetro_Z |
0.3
|
-1.307
|
0.218
|
-0.377
|
| HMC_vs_DEMetro_Z |
0.5
|
0.683
|
0.509
|
0.197
|
| HMC_vs_DEMetro_Z |
0.9
|
-0.982
|
0.347
|
-0.283
|
| HMC_vs_DEMetro_Z |
0.99
|
-0.042
|
0.967
|
-0.012
|
| Metro_vs_SMC |
0.0
|
0.385
|
0.707
|
0.111
|
| Metro_vs_SMC |
0.3
|
0.393
|
0.702
|
0.113
|
| Metro_vs_SMC |
0.5
|
1.097
|
0.296
|
0.317
|
| Metro_vs_SMC |
0.9
|
2.372
|
0.0371
|
0.685
|
| Metro_vs_SMC |
0.99
|
-0.196
|
0.848
|
-0.057
|
| DEMetro_Z_vs_SMC |
0.0
|
1.064
|
0.31
|
0.307
|
| DEMetro_Z_vs_SMC |
0.3
|
1.852
|
0.091
|
0.535
|
| DEMetro_Z_vs_SMC |
0.5
|
1.565
|
0.146
|
0.452
|
| DEMetro_Z_vs_SMC |
0.9
|
3.666
|
0.00372
|
1.058
|
| DEMetro_Z_vs_SMC |
0.99
|
-0.544
|
0.597
|
-0.157
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
7.776 |
8.779 |
15.112 |
-0.066 |
| HMC |
0.3 |
3.105 |
4.691 |
4.555 |
-0.348 |
| HMC |
0.5 |
4.549 |
3.238 |
2.938 |
0.446 |
| HMC |
0.9 |
6.358 |
2.593 |
2.648 |
1.421 |
| HMC |
0.99 |
3.695 |
2.752 |
3.294 |
0.286 |
| SMC |
0.0 |
7.719 |
8.779 |
15.112 |
-0.070 |
| SMC |
0.3 |
2.437 |
4.691 |
4.555 |
-0.495 |
| SMC |
0.5 |
2.372 |
3.238 |
2.938 |
-0.295 |
| SMC |
0.9 |
4.782 |
2.593 |
2.648 |
0.826 |
| SMC |
0.99 |
4.962 |
2.752 |
3.294 |
0.671 |
| Metro |
0.0 |
7.985 |
8.779 |
15.112 |
-0.053 |
| Metro |
0.3 |
2.680 |
4.691 |
4.555 |
-0.442 |
| Metro |
0.5 |
3.324 |
3.238 |
2.938 |
0.029 |
| Metro |
0.9 |
6.328 |
2.593 |
2.648 |
1.410 |
| Metro |
0.99 |
4.475 |
2.752 |
3.294 |
0.523 |
| DEMetro_Z |
0.0 |
8.515 |
8.779 |
15.112 |
-0.017 |
| DEMetro_Z |
0.3 |
4.181 |
4.691 |
4.555 |
-0.112 |
| DEMetro_Z |
0.5 |
3.485 |
3.238 |
2.938 |
0.084 |
| DEMetro_Z |
0.9 |
7.278 |
2.593 |
2.648 |
1.769 |
| DEMetro_Z |
0.99 |
3.728 |
2.752 |
3.294 |
0.296 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
0.844 |
0.409 |
0.411 |
| HMC |
0.3 |
2.033 |
0.0615 |
1.675 |
| HMC |
0.5 |
3.414 |
0.00491 |
3.995 |
| HMC |
0.9 |
2.884 |
0.0138 |
4.140 |
| HMC |
0.99 |
2.227 |
0.037 |
1.023 |
| SMC |
0.0 |
1.271 |
0.217 |
0.534 |
| SMC |
0.3 |
-0.202 |
0.842 |
-0.096 |
| SMC |
0.5 |
0.730 |
0.473 |
0.264 |
| SMC |
0.9 |
1.709 |
0.102 |
0.800 |
| SMC |
0.99 |
1.272 |
0.22 |
0.735 |
| Metro |
0.0 |
4.696 |
0.00018 |
2.636 |
| Metro |
0.3 |
5.335 |
0.000132 |
5.190 |
| Metro |
0.5 |
3.704 |
0.00321 |
6.850 |
| Metro |
0.9 |
4.803 |
0.000464 |
7.933 |
| Metro |
0.99 |
6.244 |
4.25e-05 |
8.534 |
| DEMetro_Z |
0.0 |
5.613 |
4.31e-05 |
3.837 |
| DEMetro_Z |
0.3 |
5.131 |
0.000271 |
8.587 |
| DEMetro_Z |
0.5 |
10.539 |
7e-09 |
6.344 |
| DEMetro_Z |
0.9 |
4.241 |
0.00126 |
8.373 |
| DEMetro_Z |
0.99 |
3.577 |
0.00178 |
1.652 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0.0
|
-2.304
|
0.0417
|
-0.665
|
| Metro_vs_DEMetro_Z |
0.3
|
-1.611
|
0.136
|
-0.465
|
| Metro_vs_DEMetro_Z |
0.5
|
0.258
|
0.801
|
0.075
|
| Metro_vs_DEMetro_Z |
0.9
|
-0.158
|
0.877
|
-0.046
|
| Metro_vs_DEMetro_Z |
0.99
|
4.948
|
0.000437
|
1.428
|
| DEMetro_Z_vs_SMC |
0.0
|
6.876
|
2.67e-05
|
1.985
|
| DEMetro_Z_vs_SMC |
0.3
|
4.825
|
0.000531
|
1.393
|
| DEMetro_Z_vs_SMC |
0.5
|
9.768
|
9.35e-07
|
2.820
|
| DEMetro_Z_vs_SMC |
0.9
|
3.702
|
0.00349
|
1.069
|
| DEMetro_Z_vs_SMC |
0.99
|
1.583
|
0.142
|
0.457
|
| HMC_vs_DEMetro_Z |
0.0
|
-5.796
|
0.00012
|
-1.673
|
| HMC_vs_DEMetro_Z |
0.3
|
-3.562
|
0.00445
|
-1.028
|
| HMC_vs_DEMetro_Z |
0.5
|
-2.116
|
0.058
|
-0.611
|
| HMC_vs_DEMetro_Z |
0.9
|
-5.893
|
0.000104
|
-1.701
|
| HMC_vs_DEMetro_Z |
0.99
|
-1.000
|
0.339
|
-0.289
|
| HMC_vs_Metro |
0.0
|
-6.066
|
8.12e-05
|
-1.751
|
| HMC_vs_Metro |
0.3
|
-2.957
|
0.013
|
-0.854
|
| HMC_vs_Metro |
0.5
|
-1.200
|
0.256
|
-0.346
|
| HMC_vs_Metro |
0.9
|
-1.584
|
0.142
|
-0.457
|
| HMC_vs_Metro |
0.99
|
-5.198
|
0.000295
|
-1.501
|
| HMC_vs_SMC |
0.0
|
-0.459
|
0.655
|
-0.132
|
| HMC_vs_SMC |
0.3
|
2.218
|
0.0485
|
0.640
|
| HMC_vs_SMC |
0.5
|
3.307
|
0.00699
|
0.955
|
| HMC_vs_SMC |
0.9
|
2.286
|
0.0431
|
0.660
|
| HMC_vs_SMC |
0.99
|
0.423
|
0.68
|
0.122
|
| Metro_vs_SMC |
0.0
|
5.839
|
0.000113
|
1.686
|
| Metro_vs_SMC |
0.3
|
5.167
|
0.00031
|
1.492
|
| Metro_vs_SMC |
0.5
|
3.861
|
0.00265
|
1.114
|
| Metro_vs_SMC |
0.9
|
4.554
|
0.000824
|
1.315
|
| Metro_vs_SMC |
0.99
|
5.339
|
0.000238
|
1.541
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.138 |
0.122 |
0.038 |
0.411 |
| HMC |
0.3 |
0.152 |
0.119 |
0.020 |
1.675 |
| HMC |
0.5 |
0.205 |
0.103 |
0.025 |
3.995 |
| HMC |
0.9 |
0.210 |
0.099 |
0.027 |
4.140 |
| HMC |
0.99 |
0.187 |
0.111 |
0.074 |
1.023 |
| SMC |
0.0 |
0.142 |
0.122 |
0.038 |
0.534 |
| SMC |
0.3 |
0.117 |
0.119 |
0.020 |
-0.096 |
| SMC |
0.5 |
0.110 |
0.103 |
0.025 |
0.264 |
| SMC |
0.9 |
0.121 |
0.099 |
0.027 |
0.800 |
| SMC |
0.99 |
0.166 |
0.111 |
0.074 |
0.735 |
| Metro |
0.0 |
0.222 |
0.122 |
0.038 |
2.636 |
| Metro |
0.3 |
0.220 |
0.119 |
0.020 |
5.190 |
| Metro |
0.5 |
0.278 |
0.103 |
0.025 |
6.850 |
| Metro |
0.9 |
0.312 |
0.099 |
0.027 |
7.933 |
| Metro |
0.99 |
0.747 |
0.111 |
0.074 |
8.534 |
| DEMetro_Z |
0.0 |
0.267 |
0.122 |
0.038 |
3.837 |
| DEMetro_Z |
0.3 |
0.287 |
0.119 |
0.020 |
8.587 |
| DEMetro_Z |
0.5 |
0.265 |
0.103 |
0.025 |
6.344 |
| DEMetro_Z |
0.9 |
0.324 |
0.099 |
0.027 |
8.373 |
| DEMetro_Z |
0.99 |
0.234 |
0.111 |
0.074 |
1.652 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
1.505 |
0.147 |
0.694 |
| HMC |
0.3 |
2.533 |
0.0226 |
1.753 |
| HMC |
0.5 |
2.269 |
0.0433 |
4.324 |
| HMC |
0.9 |
2.712 |
0.0181 |
2.925 |
| HMC |
0.99 |
2.687 |
0.0195 |
3.360 |
| SMC |
0.0 |
2.180 |
0.0409 |
1.015 |
| SMC |
0.3 |
2.113 |
0.0496 |
1.262 |
| SMC |
0.5 |
1.202 |
0.242 |
0.500 |
| SMC |
0.9 |
1.180 |
0.253 |
0.637 |
| SMC |
0.99 |
2.313 |
0.0394 |
3.336 |
| Metro |
0.0 |
5.926 |
3.99e-05 |
5.100 |
| Metro |
0.3 |
5.709 |
0.000108 |
9.449 |
| Metro |
0.5 |
6.220 |
2.69e-05 |
5.659 |
| Metro |
0.9 |
4.763 |
0.000517 |
9.062 |
| Metro |
0.99 |
6.946 |
2.37e-05 |
38.614 |
| DEMetro_Z |
0.0 |
4.218 |
0.00123 |
6.440 |
| DEMetro_Z |
0.3 |
7.502 |
7.37e-06 |
10.597 |
| DEMetro_Z |
0.5 |
8.862 |
6.63e-07 |
8.566 |
| DEMetro_Z |
0.9 |
2.871 |
0.0149 |
8.111 |
| DEMetro_Z |
0.99 |
4.737 |
0.000432 |
5.402 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0.0
|
3.809
|
0.0029
|
1.100
|
| DEMetro_Z_vs_SMC |
0.3
|
5.621
|
0.000155
|
1.623
|
| DEMetro_Z_vs_SMC |
0.5
|
8.605
|
3.24e-06
|
2.484
|
| DEMetro_Z_vs_SMC |
0.9
|
2.791
|
0.0176
|
0.806
|
| DEMetro_Z_vs_SMC |
0.99
|
1.062
|
0.311
|
0.307
|
| HMC_vs_Metro |
0.0
|
-4.606
|
0.000757
|
-1.330
|
| HMC_vs_Metro |
0.3
|
-4.713
|
0.000637
|
-1.360
|
| HMC_vs_Metro |
0.5
|
-0.585
|
0.57
|
-0.169
|
| HMC_vs_Metro |
0.9
|
-2.533
|
0.0278
|
-0.731
|
| HMC_vs_Metro |
0.99
|
-6.907
|
2.57e-05
|
-1.994
|
| Metro_vs_DEMetro_Z |
0.0
|
-0.838
|
0.42
|
-0.242
|
| Metro_vs_DEMetro_Z |
0.3
|
-0.579
|
0.574
|
-0.167
|
| Metro_vs_DEMetro_Z |
0.5
|
-2.059
|
0.064
|
-0.594
|
| Metro_vs_DEMetro_Z |
0.9
|
0.260
|
0.799
|
0.075
|
| Metro_vs_DEMetro_Z |
0.99
|
6.282
|
5.98e-05
|
1.814
|
| HMC_vs_SMC |
0.0
|
-0.762
|
0.462
|
-0.220
|
| HMC_vs_SMC |
0.3
|
0.592
|
0.566
|
0.171
|
| HMC_vs_SMC |
0.5
|
1.898
|
0.0843
|
0.548
|
| HMC_vs_SMC |
0.9
|
2.455
|
0.0319
|
0.709
|
| HMC_vs_SMC |
0.99
|
0.011
|
0.991
|
0.003
|
| Metro_vs_SMC |
0.0
|
4.402
|
0.00106
|
1.271
|
| Metro_vs_SMC |
0.3
|
4.466
|
0.000954
|
1.289
|
| Metro_vs_SMC |
0.5
|
5.548
|
0.000173
|
1.601
|
| Metro_vs_SMC |
0.9
|
4.400
|
0.00106
|
1.270
|
| Metro_vs_SMC |
0.99
|
5.416
|
0.000212
|
1.563
|
| HMC_vs_DEMetro_Z |
0.0
|
-3.447
|
0.00546
|
-0.995
|
| HMC_vs_DEMetro_Z |
0.3
|
-5.750
|
0.000128
|
-1.660
|
| HMC_vs_DEMetro_Z |
0.5
|
-1.990
|
0.072
|
-0.575
|
| HMC_vs_DEMetro_Z |
0.9
|
-2.787
|
0.0177
|
-0.805
|
| HMC_vs_DEMetro_Z |
0.99
|
-1.118
|
0.287
|
-0.323
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.017 |
0.014 |
0.004 |
0.694 |
| HMC |
0.3 |
0.019 |
0.014 |
0.003 |
1.753 |
| HMC |
0.5 |
0.029 |
0.014 |
0.004 |
4.324 |
| HMC |
0.9 |
0.030 |
0.015 |
0.005 |
2.925 |
| HMC |
0.99 |
0.030 |
0.015 |
0.004 |
3.360 |
| SMC |
0.0 |
0.019 |
0.014 |
0.004 |
1.015 |
| SMC |
0.3 |
0.018 |
0.014 |
0.003 |
1.262 |
| SMC |
0.5 |
0.015 |
0.014 |
0.004 |
0.500 |
| SMC |
0.9 |
0.018 |
0.015 |
0.005 |
0.637 |
| SMC |
0.99 |
0.029 |
0.015 |
0.004 |
3.336 |
| Metro |
0.0 |
0.037 |
0.014 |
0.004 |
5.100 |
| Metro |
0.3 |
0.042 |
0.014 |
0.003 |
9.449 |
| Metro |
0.5 |
0.034 |
0.014 |
0.004 |
5.659 |
| Metro |
0.9 |
0.063 |
0.015 |
0.005 |
9.062 |
| Metro |
0.99 |
0.182 |
0.015 |
0.004 |
38.614 |
| DEMetro_Z |
0.0 |
0.043 |
0.014 |
0.004 |
6.440 |
| DEMetro_Z |
0.3 |
0.046 |
0.014 |
0.003 |
10.597 |
| DEMetro_Z |
0.5 |
0.044 |
0.014 |
0.004 |
8.566 |
| DEMetro_Z |
0.9 |
0.058 |
0.015 |
0.005 |
8.111 |
| DEMetro_Z |
0.99 |
0.038 |
0.015 |
0.004 |
5.402 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
R Hat (scatter)
Mode Transitions
One Chain results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
-0.607 |
0.551 |
-0.218 |
| HMC |
0.3 |
-0.079 |
0.938 |
-0.034 |
| HMC |
0.5 |
0.599 |
0.558 |
0.407 |
| HMC |
0.9 |
2.118 |
0.048 |
1.160 |
| HMC |
0.99 |
-0.069 |
0.946 |
-0.023 |
| SMC |
0.0 |
-1.130 |
0.274 |
-0.377 |
| SMC |
0.3 |
0.169 |
0.867 |
0.064 |
| SMC |
0.5 |
0.277 |
0.785 |
0.136 |
| SMC |
0.9 |
-0.531 |
0.601 |
-0.212 |
| SMC |
0.99 |
1.091 |
0.287 |
0.490 |
| Metro |
0.0 |
2.082 |
0.0496 |
0.948 |
| Metro |
0.3 |
1.862 |
0.0881 |
3.366 |
| Metro |
0.5 |
2.335 |
0.0315 |
1.330 |
| Metro |
0.9 |
3.784 |
0.0028 |
7.240 |
| Metro |
0.99 |
4.313 |
0.000972 |
5.482 |
| DEMetro_Z |
0.0 |
1.519 |
0.154 |
1.875 |
| DEMetro_Z |
0.3 |
2.062 |
0.0612 |
2.634 |
| DEMetro_Z |
0.5 |
4.045 |
0.000722 |
2.191 |
| DEMetro_Z |
0.9 |
1.992 |
0.07 |
3.073 |
| DEMetro_Z |
0.99 |
0.841 |
0.409 |
0.349 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0.0
|
-1.783
|
0.102
|
-0.515
|
| HMC_vs_DEMetro_Z |
0.3
|
-2.060
|
0.0639
|
-0.595
|
| HMC_vs_DEMetro_Z |
0.5
|
-2.485
|
0.0303
|
-0.717
|
| HMC_vs_DEMetro_Z |
0.9
|
-1.190
|
0.259
|
-0.344
|
| HMC_vs_DEMetro_Z |
0.99
|
-0.919
|
0.378
|
-0.265
|
| Metro_vs_SMC |
0.0
|
3.947
|
0.00229
|
1.139
|
| Metro_vs_SMC |
0.3
|
1.784
|
0.102
|
0.515
|
| Metro_vs_SMC |
0.5
|
1.614
|
0.135
|
0.466
|
| Metro_vs_SMC |
0.9
|
3.709
|
0.00345
|
1.071
|
| Metro_vs_SMC |
0.99
|
3.582
|
0.00431
|
1.034
|
| Metro_vs_DEMetro_Z |
0.0
|
-0.711
|
0.492
|
-0.205
|
| Metro_vs_DEMetro_Z |
0.3
|
0.331
|
0.747
|
0.096
|
| Metro_vs_DEMetro_Z |
0.5
|
-1.840
|
0.0928
|
-0.531
|
| Metro_vs_DEMetro_Z |
0.9
|
1.531
|
0.154
|
0.442
|
| Metro_vs_DEMetro_Z |
0.99
|
3.614
|
0.00407
|
1.043
|
| HMC_vs_Metro |
0.0
|
-3.136
|
0.00948
|
-0.905
|
| HMC_vs_Metro |
0.3
|
-1.836
|
0.0935
|
-0.530
|
| HMC_vs_Metro |
0.5
|
-1.398
|
0.19
|
-0.404
|
| HMC_vs_Metro |
0.9
|
-3.068
|
0.0107
|
-0.886
|
| HMC_vs_Metro |
0.99
|
-4.413
|
0.00104
|
-1.274
|
| HMC_vs_SMC |
0.0
|
0.531
|
0.606
|
0.153
|
| HMC_vs_SMC |
0.3
|
-0.233
|
0.82
|
-0.067
|
| HMC_vs_SMC |
0.5
|
0.350
|
0.733
|
0.101
|
| HMC_vs_SMC |
0.9
|
2.562
|
0.0264
|
0.740
|
| HMC_vs_SMC |
0.99
|
-1.347
|
0.205
|
-0.389
|
| DEMetro_Z_vs_SMC |
0.0
|
1.908
|
0.0829
|
0.551
|
| DEMetro_Z_vs_SMC |
0.3
|
1.932
|
0.0795
|
0.558
|
| DEMetro_Z_vs_SMC |
0.5
|
3.180
|
0.00876
|
0.918
|
| DEMetro_Z_vs_SMC |
0.9
|
2.439
|
0.0329
|
0.704
|
| DEMetro_Z_vs_SMC |
0.99
|
-0.328
|
0.749
|
-0.095
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.063 |
0.072 |
0.040 |
-0.218 |
| HMC |
0.3 |
0.056 |
0.058 |
0.035 |
-0.034 |
| HMC |
0.5 |
0.069 |
0.054 |
0.037 |
0.407 |
| HMC |
0.9 |
0.079 |
0.046 |
0.028 |
1.160 |
| HMC |
0.99 |
0.068 |
0.070 |
0.087 |
-0.023 |
| SMC |
0.0 |
0.057 |
0.072 |
0.040 |
-0.377 |
| SMC |
0.3 |
0.060 |
0.058 |
0.035 |
0.064 |
| SMC |
0.5 |
0.059 |
0.054 |
0.037 |
0.136 |
| SMC |
0.9 |
0.040 |
0.046 |
0.028 |
-0.212 |
| SMC |
0.99 |
0.113 |
0.070 |
0.087 |
0.490 |
| Metro |
0.0 |
0.110 |
0.072 |
0.040 |
0.948 |
| Metro |
0.3 |
0.174 |
0.058 |
0.035 |
3.366 |
| Metro |
0.5 |
0.104 |
0.054 |
0.037 |
1.330 |
| Metro |
0.9 |
0.251 |
0.046 |
0.028 |
7.240 |
| Metro |
0.99 |
0.547 |
0.070 |
0.087 |
5.482 |
| DEMetro_Z |
0.0 |
0.147 |
0.072 |
0.040 |
1.875 |
| DEMetro_Z |
0.3 |
0.148 |
0.058 |
0.035 |
2.634 |
| DEMetro_Z |
0.5 |
0.136 |
0.054 |
0.037 |
2.191 |
| DEMetro_Z |
0.9 |
0.133 |
0.046 |
0.028 |
3.073 |
| DEMetro_Z |
0.99 |
0.100 |
0.070 |
0.087 |
0.349 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
-0.148 |
0.884 |
-0.055 |
| HMC |
0.3 |
-1.972 |
0.072 |
-0.583 |
| HMC |
0.5 |
0.857 |
0.409 |
1.900 |
| HMC |
0.9 |
1.653 |
0.121 |
1.408 |
| HMC |
0.99 |
0.682 |
0.503 |
0.262 |
| SMC |
0.0 |
0.002 |
0.998 |
0.001 |
| SMC |
0.3 |
0.007 |
0.994 |
0.004 |
| SMC |
0.5 |
0.961 |
0.357 |
10.679 |
| SMC |
0.9 |
1.263 |
0.227 |
0.993 |
| SMC |
0.99 |
0.805 |
0.431 |
0.440 |
| Metro |
0.0 |
-0.176 |
0.862 |
-0.067 |
| Metro |
0.3 |
0.345 |
0.734 |
0.199 |
| Metro |
0.5 |
-0.665 |
0.515 |
-0.222 |
| Metro |
0.9 |
2.121 |
0.0523 |
1.748 |
| Metro |
0.99 |
1.333 |
0.197 |
0.484 |
| DEMetro_Z |
0.0 |
0.048 |
0.962 |
0.019 |
| DEMetro_Z |
0.3 |
-0.096 |
0.925 |
-0.045 |
| DEMetro_Z |
0.5 |
0.156 |
0.878 |
0.049 |
| DEMetro_Z |
0.9 |
2.457 |
0.0286 |
2.354 |
| DEMetro_Z |
0.99 |
0.750 |
0.462 |
0.270 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0.0
|
-0.620
|
0.548
|
-0.179
|
| HMC_vs_SMC |
0.3
|
-1.022
|
0.329
|
-0.295
|
| HMC_vs_SMC |
0.5
|
-0.762
|
0.462
|
-0.220
|
| HMC_vs_SMC |
0.9
|
2.240
|
0.0467
|
0.647
|
| HMC_vs_SMC |
0.99
|
-0.290
|
0.777
|
-0.084
|
| Metro_vs_DEMetro_Z |
0.0
|
-3.537
|
0.00466
|
-1.021
|
| Metro_vs_DEMetro_Z |
0.3
|
0.361
|
0.725
|
0.104
|
| Metro_vs_DEMetro_Z |
0.5
|
-3.009
|
0.0119
|
-0.869
|
| Metro_vs_DEMetro_Z |
0.9
|
-0.938
|
0.368
|
-0.271
|
| Metro_vs_DEMetro_Z |
0.99
|
1.255
|
0.235
|
0.362
|
| HMC_vs_Metro |
0.0
|
0.202
|
0.844
|
0.058
|
| HMC_vs_Metro |
0.3
|
-1.526
|
0.155
|
-0.441
|
| HMC_vs_Metro |
0.5
|
0.962
|
0.357
|
0.278
|
| HMC_vs_Metro |
0.9
|
-1.227
|
0.246
|
-0.354
|
| HMC_vs_Metro |
0.99
|
-0.787
|
0.448
|
-0.227
|
| HMC_vs_DEMetro_Z |
0.0
|
-1.349
|
0.205
|
-0.389
|
| HMC_vs_DEMetro_Z |
0.3
|
-1.555
|
0.148
|
-0.449
|
| HMC_vs_DEMetro_Z |
0.5
|
0.849
|
0.414
|
0.245
|
| HMC_vs_DEMetro_Z |
0.9
|
-1.434
|
0.179
|
-0.414
|
| HMC_vs_DEMetro_Z |
0.99
|
-0.029
|
0.977
|
-0.008
|
| Metro_vs_SMC |
0.0
|
-1.061
|
0.311
|
-0.306
|
| Metro_vs_SMC |
0.3
|
0.236
|
0.818
|
0.068
|
| Metro_vs_SMC |
0.5
|
-0.982
|
0.347
|
-0.284
|
| Metro_vs_SMC |
0.9
|
3.894
|
0.0025
|
1.124
|
| Metro_vs_SMC |
0.99
|
0.089
|
0.93
|
0.026
|
| DEMetro_Z_vs_SMC |
0.0
|
0.292
|
0.776
|
0.084
|
| DEMetro_Z_vs_SMC |
0.3
|
-0.073
|
0.943
|
-0.021
|
| DEMetro_Z_vs_SMC |
0.5
|
-0.958
|
0.358
|
-0.277
|
| DEMetro_Z_vs_SMC |
0.9
|
2.035
|
0.0666
|
0.588
|
| DEMetro_Z_vs_SMC |
0.99
|
-0.341
|
0.739
|
-0.099
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
7.948 |
8.779 |
15.112 |
-0.055 |
| HMC |
0.3 |
2.035 |
4.691 |
4.555 |
-0.583 |
| HMC |
0.5 |
8.820 |
3.238 |
2.938 |
1.900 |
| HMC |
0.9 |
6.321 |
2.593 |
2.648 |
1.408 |
| HMC |
0.99 |
3.615 |
2.752 |
3.294 |
0.262 |
| SMC |
0.0 |
8.792 |
8.779 |
15.112 |
0.001 |
| SMC |
0.3 |
4.711 |
4.691 |
4.555 |
0.004 |
| SMC |
0.5 |
34.612 |
3.238 |
2.938 |
10.679 |
| SMC |
0.9 |
5.224 |
2.593 |
2.648 |
0.993 |
| SMC |
0.99 |
4.200 |
2.752 |
3.294 |
0.440 |
| Metro |
0.0 |
7.764 |
8.779 |
15.112 |
-0.067 |
| Metro |
0.3 |
5.596 |
4.691 |
4.555 |
0.199 |
| Metro |
0.5 |
2.585 |
3.238 |
2.938 |
-0.222 |
| Metro |
0.9 |
7.223 |
2.593 |
2.648 |
1.748 |
| Metro |
0.99 |
4.348 |
2.752 |
3.294 |
0.484 |
| DEMetro_Z |
0.0 |
9.060 |
8.779 |
15.112 |
0.019 |
| DEMetro_Z |
0.3 |
4.486 |
4.691 |
4.555 |
-0.045 |
| DEMetro_Z |
0.5 |
3.382 |
3.238 |
2.938 |
0.049 |
| DEMetro_Z |
0.9 |
8.829 |
2.593 |
2.648 |
2.354 |
| DEMetro_Z |
0.99 |
3.641 |
2.752 |
3.294 |
0.270 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
1.056 |
0.302 |
0.430 |
| HMC |
0.3 |
0.711 |
0.488 |
0.510 |
| HMC |
0.5 |
1.727 |
0.11 |
2.603 |
| HMC |
0.9 |
5.886 |
1.12e-05 |
3.074 |
| HMC |
0.99 |
2.170 |
0.0414 |
0.824 |
| SMC |
0.0 |
0.396 |
0.696 |
0.180 |
| SMC |
0.3 |
-0.069 |
0.946 |
-0.035 |
| SMC |
0.5 |
1.287 |
0.221 |
1.333 |
| SMC |
0.9 |
0.379 |
0.709 |
0.142 |
| SMC |
0.99 |
1.059 |
0.302 |
0.487 |
| Metro |
0.0 |
3.909 |
0.000855 |
1.903 |
| Metro |
0.3 |
2.678 |
0.0211 |
7.315 |
| Metro |
0.5 |
6.626 |
1.95e-06 |
3.304 |
| Metro |
0.9 |
6.106 |
5.85e-05 |
9.905 |
| Metro |
0.99 |
7.875 |
3.15e-06 |
8.560 |
| DEMetro_Z |
0.0 |
3.597 |
0.00345 |
4.109 |
| DEMetro_Z |
0.3 |
4.131 |
0.00152 |
7.812 |
| DEMetro_Z |
0.5 |
10.965 |
4.39e-10 |
5.163 |
| DEMetro_Z |
0.9 |
3.017 |
0.0112 |
6.197 |
| DEMetro_Z |
0.99 |
5.066 |
4.58e-05 |
1.984 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0.0
|
-1.951
|
0.077
|
-0.563
|
| Metro_vs_DEMetro_Z |
0.3
|
-0.140
|
0.891
|
-0.040
|
| Metro_vs_DEMetro_Z |
0.5
|
-3.939
|
0.00231
|
-1.137
|
| Metro_vs_DEMetro_Z |
0.9
|
1.373
|
0.197
|
0.396
|
| Metro_vs_DEMetro_Z |
0.99
|
5.965
|
9.38e-05
|
1.722
|
| DEMetro_Z_vs_SMC |
0.0
|
3.501
|
0.00496
|
1.011
|
| DEMetro_Z_vs_SMC |
0.3
|
4.003
|
0.00208
|
1.156
|
| DEMetro_Z_vs_SMC |
0.5
|
3.859
|
0.00266
|
1.114
|
| DEMetro_Z_vs_SMC |
0.9
|
3.043
|
0.0112
|
0.878
|
| DEMetro_Z_vs_SMC |
0.99
|
3.271
|
0.00745
|
0.944
|
| HMC_vs_DEMetro_Z |
0.0
|
-3.181
|
0.00874
|
-0.918
|
| HMC_vs_DEMetro_Z |
0.3
|
-3.645
|
0.00385
|
-1.052
|
| HMC_vs_DEMetro_Z |
0.5
|
-1.718
|
0.114
|
-0.496
|
| HMC_vs_DEMetro_Z |
0.9
|
-1.502
|
0.161
|
-0.434
|
| HMC_vs_DEMetro_Z |
0.99
|
-3.421
|
0.00571
|
-0.988
|
| HMC_vs_Metro |
0.0
|
-4.757
|
0.000593
|
-1.373
|
| HMC_vs_Metro |
0.3
|
-2.282
|
0.0434
|
-0.659
|
| HMC_vs_Metro |
0.5
|
-0.510
|
0.62
|
-0.147
|
| HMC_vs_Metro |
0.9
|
-3.971
|
0.00219
|
-1.146
|
| HMC_vs_Metro |
0.99
|
-7.617
|
1.04e-05
|
-2.199
|
| HMC_vs_SMC |
0.0
|
0.897
|
0.389
|
0.259
|
| HMC_vs_SMC |
0.3
|
0.678
|
0.512
|
0.196
|
| HMC_vs_SMC |
0.5
|
0.696
|
0.501
|
0.201
|
| HMC_vs_SMC |
0.9
|
6.317
|
5.7e-05
|
1.823
|
| HMC_vs_SMC |
0.99
|
0.644
|
0.533
|
0.186
|
| Metro_vs_SMC |
0.0
|
5.488
|
0.00019
|
1.584
|
| Metro_vs_SMC |
0.3
|
2.496
|
0.0297
|
0.720
|
| Metro_vs_SMC |
0.5
|
1.701
|
0.117
|
0.491
|
| Metro_vs_SMC |
0.9
|
6.144
|
7.27e-05
|
1.774
|
| Metro_vs_SMC |
0.99
|
6.588
|
3.93e-05
|
1.902
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.138 |
0.122 |
0.038 |
0.430 |
| HMC |
0.3 |
0.129 |
0.119 |
0.020 |
0.510 |
| HMC |
0.5 |
0.170 |
0.103 |
0.025 |
2.603 |
| HMC |
0.9 |
0.182 |
0.099 |
0.027 |
3.074 |
| HMC |
0.99 |
0.172 |
0.111 |
0.074 |
0.824 |
| SMC |
0.0 |
0.129 |
0.122 |
0.038 |
0.180 |
| SMC |
0.3 |
0.118 |
0.119 |
0.020 |
-0.035 |
| SMC |
0.5 |
0.137 |
0.103 |
0.025 |
1.333 |
| SMC |
0.9 |
0.103 |
0.099 |
0.027 |
0.142 |
| SMC |
0.99 |
0.147 |
0.111 |
0.074 |
0.487 |
| Metro |
0.0 |
0.194 |
0.122 |
0.038 |
1.903 |
| Metro |
0.3 |
0.262 |
0.119 |
0.020 |
7.315 |
| Metro |
0.5 |
0.188 |
0.103 |
0.025 |
3.304 |
| Metro |
0.9 |
0.365 |
0.099 |
0.027 |
9.905 |
| Metro |
0.99 |
0.749 |
0.111 |
0.074 |
8.560 |
| DEMetro_Z |
0.0 |
0.277 |
0.122 |
0.038 |
4.109 |
| DEMetro_Z |
0.3 |
0.272 |
0.119 |
0.020 |
7.812 |
| DEMetro_Z |
0.5 |
0.235 |
0.103 |
0.025 |
5.163 |
| DEMetro_Z |
0.9 |
0.265 |
0.099 |
0.027 |
6.197 |
| DEMetro_Z |
0.99 |
0.259 |
0.111 |
0.074 |
1.984 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
2.221 |
0.0373 |
0.998 |
| HMC |
0.3 |
2.019 |
0.0635 |
1.756 |
| HMC |
0.5 |
3.606 |
0.00184 |
1.854 |
| HMC |
0.9 |
2.895 |
0.00998 |
1.724 |
| HMC |
0.99 |
4.503 |
0.000473 |
3.570 |
| SMC |
0.0 |
0.043 |
0.966 |
0.019 |
| SMC |
0.3 |
1.522 |
0.146 |
0.908 |
| SMC |
0.5 |
2.324 |
0.0347 |
1.713 |
| SMC |
0.9 |
-0.126 |
0.901 |
-0.049 |
| SMC |
0.99 |
2.757 |
0.0163 |
2.704 |
| Metro |
0.0 |
4.289 |
0.000864 |
4.157 |
| Metro |
0.3 |
6.227 |
3.05e-05 |
6.165 |
| Metro |
0.5 |
6.873 |
8.78e-06 |
6.023 |
| Metro |
0.9 |
4.737 |
0.000561 |
10.792 |
| Metro |
0.99 |
5.931 |
9.78e-05 |
55.272 |
| DEMetro_Z |
0.0 |
3.486 |
0.00483 |
7.361 |
| DEMetro_Z |
0.3 |
6.091 |
5.26e-05 |
8.117 |
| DEMetro_Z |
0.5 |
8.487 |
2.26e-07 |
5.437 |
| DEMetro_Z |
0.9 |
4.978 |
0.000152 |
3.445 |
| DEMetro_Z |
0.99 |
6.175 |
4.35e-05 |
7.679 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0.0
|
3.322
|
0.00681
|
0.959
|
| DEMetro_Z_vs_SMC |
0.3
|
5.503
|
0.000185
|
1.589
|
| DEMetro_Z_vs_SMC |
0.5
|
3.793
|
0.00298
|
1.095
|
| DEMetro_Z_vs_SMC |
0.9
|
5.036
|
0.00038
|
1.454
|
| DEMetro_Z_vs_SMC |
0.99
|
3.331
|
0.0067
|
0.962
|
| HMC_vs_Metro |
0.0
|
-3.330
|
0.00671
|
-0.961
|
| HMC_vs_Metro |
0.3
|
-3.105
|
0.01
|
-0.896
|
| HMC_vs_Metro |
0.5
|
-4.864
|
0.0005
|
-1.404
|
| HMC_vs_Metro |
0.9
|
-3.823
|
0.00283
|
-1.104
|
| HMC_vs_Metro |
0.99
|
-5.774
|
0.000124
|
-1.667
|
| Metro_vs_DEMetro_Z |
0.0
|
-1.361
|
0.201
|
-0.393
|
| Metro_vs_DEMetro_Z |
0.3
|
-1.025
|
0.327
|
-0.296
|
| Metro_vs_DEMetro_Z |
0.5
|
0.514
|
0.618
|
0.148
|
| Metro_vs_DEMetro_Z |
0.9
|
3.145
|
0.00932
|
0.908
|
| Metro_vs_DEMetro_Z |
0.99
|
5.091
|
0.000349
|
1.470
|
| HMC_vs_SMC |
0.0
|
2.575
|
0.0258
|
0.743
|
| HMC_vs_SMC |
0.3
|
0.768
|
0.459
|
0.222
|
| HMC_vs_SMC |
0.5
|
0.217
|
0.832
|
0.063
|
| HMC_vs_SMC |
0.9
|
2.610
|
0.0243
|
0.753
|
| HMC_vs_SMC |
0.99
|
0.672
|
0.515
|
0.194
|
| Metro_vs_SMC |
0.0
|
4.613
|
0.000749
|
1.332
|
| Metro_vs_SMC |
0.3
|
4.159
|
0.00159
|
1.201
|
| Metro_vs_SMC |
0.5
|
3.688
|
0.00358
|
1.065
|
| Metro_vs_SMC |
0.9
|
4.597
|
0.000769
|
1.327
|
| Metro_vs_SMC |
0.99
|
5.517
|
0.000181
|
1.593
|
| HMC_vs_DEMetro_Z |
0.0
|
-3.053
|
0.011
|
-0.881
|
| HMC_vs_DEMetro_Z |
0.3
|
-3.601
|
0.00416
|
-1.040
|
| HMC_vs_DEMetro_Z |
0.5
|
-6.097
|
7.77e-05
|
-1.760
|
| HMC_vs_DEMetro_Z |
0.9
|
-2.222
|
0.0482
|
-0.641
|
| HMC_vs_DEMetro_Z |
0.99
|
-3.374
|
0.00621
|
-0.974
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.019 |
0.014 |
0.004 |
0.998 |
| HMC |
0.3 |
0.019 |
0.014 |
0.003 |
1.756 |
| HMC |
0.5 |
0.020 |
0.014 |
0.004 |
1.854 |
| HMC |
0.9 |
0.024 |
0.015 |
0.005 |
1.724 |
| HMC |
0.99 |
0.030 |
0.015 |
0.004 |
3.570 |
| SMC |
0.0 |
0.015 |
0.014 |
0.004 |
0.019 |
| SMC |
0.3 |
0.017 |
0.014 |
0.003 |
0.908 |
| SMC |
0.5 |
0.020 |
0.014 |
0.004 |
1.713 |
| SMC |
0.9 |
0.015 |
0.015 |
0.005 |
-0.049 |
| SMC |
0.99 |
0.027 |
0.015 |
0.004 |
2.704 |
| Metro |
0.0 |
0.033 |
0.014 |
0.004 |
4.157 |
| Metro |
0.3 |
0.033 |
0.014 |
0.003 |
6.165 |
| Metro |
0.5 |
0.035 |
0.014 |
0.004 |
6.023 |
| Metro |
0.9 |
0.072 |
0.015 |
0.005 |
10.792 |
| Metro |
0.99 |
0.254 |
0.015 |
0.004 |
55.272 |
| DEMetro_Z |
0.0 |
0.047 |
0.014 |
0.004 |
7.361 |
| DEMetro_Z |
0.3 |
0.038 |
0.014 |
0.003 |
8.117 |
| DEMetro_Z |
0.5 |
0.033 |
0.014 |
0.004 |
5.437 |
| DEMetro_Z |
0.9 |
0.033 |
0.015 |
0.005 |
3.445 |
| DEMetro_Z |
0.99 |
0.048 |
0.015 |
0.004 |
7.679 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
Mode Transitions
KDE + Init Plots
Forest & Ridge Plots
Pooled
Chain
Pairwise Scatter Plots
Pooled
Chain
Vary_Correlation_with_high_Multimodality
(Mixture,
correlation,
12 runs)
Pooled Chains results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
4.017 |
0.00201 |
30.053 |
| HMC |
0.3 |
4.600 |
0.000759 |
34.242 |
| HMC |
0.5 |
2.200 |
0.0501 |
24.498 |
| HMC |
0.9 |
4.145 |
0.00162 |
27.478 |
| HMC |
0.99 |
2.899 |
0.0145 |
37.866 |
| SMC |
0.0 |
0.159 |
0.875 |
0.069 |
| SMC |
0.3 |
0.942 |
0.357 |
0.450 |
| SMC |
0.5 |
0.448 |
0.66 |
0.152 |
| SMC |
0.9 |
0.978 |
0.34 |
0.463 |
| SMC |
0.99 |
0.554 |
0.586 |
0.289 |
| Metro |
0.0 |
3.453 |
0.00538 |
26.777 |
| Metro |
0.3 |
4.008 |
0.00204 |
26.862 |
| Metro |
0.5 |
2.850 |
0.0158 |
23.856 |
| Metro |
0.9 |
4.367 |
0.00111 |
28.000 |
| Metro |
0.99 |
3.660 |
0.00374 |
44.643 |
| DEMetro_Z |
0.0 |
4.528 |
0.000855 |
37.040 |
| DEMetro_Z |
0.3 |
4.657 |
0.000687 |
25.453 |
| DEMetro_Z |
0.5 |
3.700 |
0.00349 |
44.902 |
| DEMetro_Z |
0.9 |
4.080 |
0.00181 |
27.284 |
| DEMetro_Z |
0.99 |
3.940 |
0.00231 |
53.457 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0.0
|
-0.558
|
0.588
|
-0.161
|
| HMC_vs_DEMetro_Z |
0.3
|
0.863
|
0.407
|
0.249
|
| HMC_vs_DEMetro_Z |
0.5
|
-1.405
|
0.188
|
-0.406
|
| HMC_vs_DEMetro_Z |
0.9
|
0.021
|
0.984
|
0.006
|
| HMC_vs_DEMetro_Z |
0.99
|
-0.881
|
0.397
|
-0.254
|
| Metro_vs_SMC |
0.0
|
3.464
|
0.0053
|
1.000
|
| Metro_vs_SMC |
0.3
|
4.052
|
0.00191
|
1.170
|
| Metro_vs_SMC |
0.5
|
2.863
|
0.0154
|
0.826
|
| Metro_vs_SMC |
0.9
|
4.161
|
0.00159
|
1.201
|
| Metro_vs_SMC |
0.99
|
3.563
|
0.00445
|
1.028
|
| Metro_vs_DEMetro_Z |
0.0
|
-0.875
|
0.4
|
-0.252
|
| Metro_vs_DEMetro_Z |
0.3
|
0.144
|
0.888
|
0.042
|
| Metro_vs_DEMetro_Z |
0.5
|
-1.323
|
0.213
|
-0.382
|
| Metro_vs_DEMetro_Z |
0.9
|
0.081
|
0.937
|
0.023
|
| Metro_vs_DEMetro_Z |
0.99
|
-0.584
|
0.571
|
-0.168
|
| HMC_vs_Metro |
0.0
|
0.940
|
0.368
|
0.271
|
| HMC_vs_Metro |
0.3
|
0.954
|
0.361
|
0.275
|
| HMC_vs_Metro |
0.5
|
0.041
|
0.968
|
0.012
|
| HMC_vs_Metro |
0.9
|
-0.083
|
0.936
|
-0.024
|
| HMC_vs_Metro |
0.99
|
-0.335
|
0.744
|
-0.097
|
| HMC_vs_SMC |
0.0
|
4.035
|
0.00197
|
1.165
|
| HMC_vs_SMC |
0.3
|
4.675
|
0.000677
|
1.350
|
| HMC_vs_SMC |
0.5
|
2.170
|
0.0528
|
0.626
|
| HMC_vs_SMC |
0.9
|
4.011
|
0.00205
|
1.158
|
| HMC_vs_SMC |
0.99
|
2.895
|
0.0146
|
0.836
|
| DEMetro_Z_vs_SMC |
0.0
|
4.494
|
0.000911
|
1.297
|
| DEMetro_Z_vs_SMC |
0.3
|
4.575
|
0.000796
|
1.321
|
| DEMetro_Z_vs_SMC |
0.5
|
3.667
|
0.00371
|
1.059
|
| DEMetro_Z_vs_SMC |
0.9
|
4.011
|
0.00205
|
1.158
|
| DEMetro_Z_vs_SMC |
0.99
|
3.929
|
0.00235
|
1.134
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
1.743 |
0.092 |
0.055 |
30.053 |
| HMC |
0.3 |
2.090 |
0.101 |
0.058 |
34.242 |
| HMC |
0.5 |
1.008 |
0.046 |
0.039 |
24.498 |
| HMC |
0.9 |
1.743 |
0.074 |
0.061 |
27.478 |
| HMC |
0.99 |
1.545 |
0.079 |
0.039 |
37.866 |
| SMC |
0.0 |
0.096 |
0.092 |
0.055 |
0.069 |
| SMC |
0.3 |
0.127 |
0.101 |
0.058 |
0.450 |
| SMC |
0.5 |
0.052 |
0.046 |
0.039 |
0.152 |
| SMC |
0.9 |
0.102 |
0.074 |
0.061 |
0.463 |
| SMC |
0.99 |
0.090 |
0.079 |
0.039 |
0.289 |
| Metro |
0.0 |
1.563 |
0.092 |
0.055 |
26.777 |
| Metro |
0.3 |
1.661 |
0.101 |
0.058 |
26.862 |
| Metro |
0.5 |
0.983 |
0.046 |
0.039 |
23.856 |
| Metro |
0.9 |
1.774 |
0.074 |
0.061 |
28.000 |
| Metro |
0.99 |
1.808 |
0.079 |
0.039 |
44.643 |
| DEMetro_Z |
0.0 |
2.126 |
0.092 |
0.055 |
37.040 |
| DEMetro_Z |
0.3 |
1.579 |
0.101 |
0.058 |
25.453 |
| DEMetro_Z |
0.5 |
1.810 |
0.046 |
0.039 |
44.902 |
| DEMetro_Z |
0.9 |
1.731 |
0.074 |
0.061 |
27.284 |
| DEMetro_Z |
0.99 |
2.149 |
0.079 |
0.039 |
53.457 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
2.883 |
0.0149 |
46.926 |
| HMC |
0.3 |
3.141 |
0.00939 |
66.429 |
| HMC |
0.5 |
1.737 |
0.11 |
47.528 |
| HMC |
0.9 |
2.942 |
0.0134 |
72.980 |
| HMC |
0.99 |
2.314 |
0.041 |
60.419 |
| SMC |
0.0 |
0.408 |
0.688 |
0.169 |
| SMC |
0.3 |
0.189 |
0.852 |
0.074 |
| SMC |
0.5 |
1.148 |
0.27 |
0.969 |
| SMC |
0.9 |
1.006 |
0.328 |
0.603 |
| SMC |
0.99 |
-1.489 |
0.151 |
-0.597 |
| Metro |
0.0 |
2.571 |
0.026 |
43.000 |
| Metro |
0.3 |
2.769 |
0.0182 |
46.661 |
| Metro |
0.5 |
3.024 |
0.0116 |
34.131 |
| Metro |
0.9 |
3.042 |
0.0112 |
73.981 |
| Metro |
0.99 |
3.077 |
0.0105 |
74.455 |
| DEMetro_Z |
0.0 |
2.920 |
0.0139 |
66.382 |
| DEMetro_Z |
0.3 |
2.454 |
0.032 |
37.863 |
| DEMetro_Z |
0.5 |
2.872 |
0.0152 |
92.045 |
| DEMetro_Z |
0.9 |
2.952 |
0.0132 |
72.746 |
| DEMetro_Z |
0.99 |
3.002 |
0.012 |
86.033 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0.0
|
2.851
|
0.0158
|
0.823
|
| HMC_vs_SMC |
0.3
|
3.137
|
0.00947
|
0.905
|
| HMC_vs_SMC |
0.5
|
1.688
|
0.119
|
0.487
|
| HMC_vs_SMC |
0.9
|
2.894
|
0.0146
|
0.835
|
| HMC_vs_SMC |
0.99
|
2.358
|
0.038
|
0.681
|
| Metro_vs_DEMetro_Z |
0.0
|
-0.817
|
0.431
|
-0.236
|
| Metro_vs_DEMetro_Z |
0.3
|
0.366
|
0.722
|
0.106
|
| Metro_vs_DEMetro_Z |
0.5
|
-1.610
|
0.136
|
-0.465
|
| Metro_vs_DEMetro_Z |
0.9
|
0.033
|
0.974
|
0.010
|
| Metro_vs_DEMetro_Z |
0.99
|
-0.484
|
0.638
|
-0.140
|
| HMC_vs_Metro |
0.0
|
1.016
|
0.331
|
0.293
|
| HMC_vs_Metro |
0.3
|
1.241
|
0.24
|
0.358
|
| HMC_vs_Metro |
0.5
|
0.413
|
0.688
|
0.119
|
| HMC_vs_Metro |
0.9
|
-0.073
|
0.943
|
-0.021
|
| HMC_vs_Metro |
0.99
|
-0.352
|
0.731
|
-0.102
|
| HMC_vs_DEMetro_Z |
0.0
|
-0.665
|
0.519
|
-0.192
|
| HMC_vs_DEMetro_Z |
0.3
|
0.996
|
0.341
|
0.287
|
| HMC_vs_DEMetro_Z |
0.5
|
-1.042
|
0.32
|
-0.301
|
| HMC_vs_DEMetro_Z |
0.9
|
0.006
|
0.995
|
0.002
|
| HMC_vs_DEMetro_Z |
0.99
|
-0.731
|
0.48
|
-0.211
|
| Metro_vs_SMC |
0.0
|
2.543
|
0.0273
|
0.734
|
| Metro_vs_SMC |
0.3
|
2.779
|
0.018
|
0.802
|
| Metro_vs_SMC |
0.5
|
2.878
|
0.015
|
0.831
|
| Metro_vs_SMC |
0.9
|
3.005
|
0.012
|
0.868
|
| Metro_vs_SMC |
0.99
|
3.094
|
0.0102
|
0.893
|
| DEMetro_Z_vs_SMC |
0.0
|
2.917
|
0.014
|
0.842
|
| DEMetro_Z_vs_SMC |
0.3
|
2.428
|
0.0335
|
0.701
|
| DEMetro_Z_vs_SMC |
0.5
|
2.817
|
0.0167
|
0.813
|
| DEMetro_Z_vs_SMC |
0.9
|
2.930
|
0.0137
|
0.846
|
| DEMetro_Z_vs_SMC |
0.99
|
3.030
|
0.0114
|
0.875
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
6.875 |
0.187 |
0.143 |
46.926 |
| HMC |
0.3 |
9.308 |
0.190 |
0.137 |
66.429 |
| HMC |
0.5 |
4.457 |
0.144 |
0.091 |
47.528 |
| HMC |
0.9 |
6.925 |
0.111 |
0.093 |
72.980 |
| HMC |
0.99 |
7.546 |
0.199 |
0.122 |
60.419 |
| SMC |
0.0 |
0.211 |
0.187 |
0.143 |
0.169 |
| SMC |
0.3 |
0.200 |
0.190 |
0.137 |
0.074 |
| SMC |
0.5 |
0.232 |
0.144 |
0.091 |
0.969 |
| SMC |
0.9 |
0.167 |
0.111 |
0.093 |
0.603 |
| SMC |
0.99 |
0.126 |
0.199 |
0.122 |
-0.597 |
| Metro |
0.0 |
6.316 |
0.187 |
0.143 |
43.000 |
| Metro |
0.3 |
6.595 |
0.190 |
0.137 |
46.661 |
| Metro |
0.5 |
3.241 |
0.144 |
0.091 |
34.131 |
| Metro |
0.9 |
7.019 |
0.111 |
0.093 |
73.981 |
| Metro |
0.99 |
9.252 |
0.199 |
0.122 |
74.455 |
| DEMetro_Z |
0.0 |
9.649 |
0.187 |
0.143 |
66.382 |
| DEMetro_Z |
0.3 |
5.387 |
0.190 |
0.137 |
37.863 |
| DEMetro_Z |
0.5 |
8.498 |
0.144 |
0.091 |
92.045 |
| DEMetro_Z |
0.9 |
6.903 |
0.111 |
0.093 |
72.746 |
| DEMetro_Z |
0.99 |
10.660 |
0.199 |
0.122 |
86.033 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
3.830 |
0.00278 |
34.209 |
| HMC |
0.3 |
4.709 |
0.000635 |
33.350 |
| HMC |
0.5 |
2.109 |
0.0587 |
27.856 |
| HMC |
0.9 |
4.103 |
0.00174 |
28.141 |
| HMC |
0.99 |
2.884 |
0.0148 |
39.222 |
| SMC |
0.0 |
-0.016 |
0.988 |
-0.007 |
| SMC |
0.3 |
0.978 |
0.339 |
0.457 |
| SMC |
0.5 |
0.208 |
0.838 |
0.074 |
| SMC |
0.9 |
0.866 |
0.396 |
0.399 |
| SMC |
0.99 |
0.279 |
0.783 |
0.141 |
| Metro |
0.0 |
3.534 |
0.00467 |
31.336 |
| Metro |
0.3 |
3.820 |
0.00283 |
26.251 |
| Metro |
0.5 |
2.884 |
0.0148 |
26.805 |
| Metro |
0.9 |
4.613 |
0.000741 |
29.498 |
| Metro |
0.99 |
4.014 |
0.00203 |
48.651 |
| DEMetro_Z |
0.0 |
4.442 |
0.000987 |
44.517 |
| DEMetro_Z |
0.3 |
4.425 |
0.00101 |
26.599 |
| DEMetro_Z |
0.5 |
3.628 |
0.00396 |
51.562 |
| DEMetro_Z |
0.9 |
4.267 |
0.00132 |
27.851 |
| DEMetro_Z |
0.99 |
4.012 |
0.00204 |
55.657 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0.0
|
-0.932
|
0.372
|
-0.269
|
| Metro_vs_DEMetro_Z |
0.3
|
-0.035
|
0.973
|
-0.010
|
| Metro_vs_DEMetro_Z |
0.5
|
-1.327
|
0.211
|
-0.383
|
| Metro_vs_DEMetro_Z |
0.9
|
0.186
|
0.856
|
0.054
|
| Metro_vs_DEMetro_Z |
0.99
|
-0.482
|
0.639
|
-0.139
|
| DEMetro_Z_vs_SMC |
0.0
|
4.403
|
0.00106
|
1.271
|
| DEMetro_Z_vs_SMC |
0.3
|
4.324
|
0.00121
|
1.248
|
| DEMetro_Z_vs_SMC |
0.5
|
3.600
|
0.00417
|
1.039
|
| DEMetro_Z_vs_SMC |
0.9
|
4.198
|
0.00149
|
1.212
|
| DEMetro_Z_vs_SMC |
0.99
|
4.017
|
0.00203
|
1.160
|
| HMC_vs_DEMetro_Z |
0.0
|
-0.697
|
0.5
|
-0.201
|
| HMC_vs_DEMetro_Z |
0.3
|
0.648
|
0.53
|
0.187
|
| HMC_vs_DEMetro_Z |
0.5
|
-1.389
|
0.192
|
-0.401
|
| HMC_vs_DEMetro_Z |
0.9
|
0.030
|
0.976
|
0.009
|
| HMC_vs_DEMetro_Z |
0.99
|
-0.904
|
0.385
|
-0.261
|
| HMC_vs_Metro |
0.0
|
0.709
|
0.493
|
0.205
|
| HMC_vs_Metro |
0.3
|
0.916
|
0.379
|
0.264
|
| HMC_vs_Metro |
0.5
|
0.058
|
0.955
|
0.017
|
| HMC_vs_Metro |
0.9
|
-0.198
|
0.847
|
-0.057
|
| HMC_vs_Metro |
0.99
|
-0.465
|
0.651
|
-0.134
|
| HMC_vs_SMC |
0.0
|
3.842
|
0.00274
|
1.109
|
| HMC_vs_SMC |
0.3
|
4.792
|
0.000561
|
1.383
|
| HMC_vs_SMC |
0.5
|
2.090
|
0.0606
|
0.603
|
| HMC_vs_SMC |
0.9
|
3.991
|
0.00212
|
1.152
|
| HMC_vs_SMC |
0.99
|
2.898
|
0.0145
|
0.837
|
| Metro_vs_SMC |
0.0
|
3.548
|
0.00457
|
1.024
|
| Metro_vs_SMC |
0.3
|
3.878
|
0.00257
|
1.119
|
| Metro_vs_SMC |
0.5
|
2.888
|
0.0148
|
0.834
|
| Metro_vs_SMC |
0.9
|
4.426
|
0.00102
|
1.278
|
| Metro_vs_SMC |
0.99
|
3.925
|
0.00237
|
1.133
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
1.537 |
0.101 |
0.042 |
34.209 |
| HMC |
0.3 |
1.810 |
0.108 |
0.051 |
33.350 |
| HMC |
0.5 |
0.913 |
0.065 |
0.030 |
27.856 |
| HMC |
0.9 |
1.547 |
0.084 |
0.052 |
28.141 |
| HMC |
0.99 |
1.413 |
0.092 |
0.034 |
39.222 |
| SMC |
0.0 |
0.100 |
0.101 |
0.042 |
-0.007 |
| SMC |
0.3 |
0.131 |
0.108 |
0.051 |
0.457 |
| SMC |
0.5 |
0.067 |
0.065 |
0.030 |
0.074 |
| SMC |
0.9 |
0.104 |
0.084 |
0.052 |
0.399 |
| SMC |
0.99 |
0.097 |
0.092 |
0.034 |
0.141 |
| Metro |
0.0 |
1.416 |
0.101 |
0.042 |
31.336 |
| Metro |
0.3 |
1.448 |
0.108 |
0.051 |
26.251 |
| Metro |
0.5 |
0.881 |
0.065 |
0.030 |
26.805 |
| Metro |
0.9 |
1.618 |
0.084 |
0.052 |
29.498 |
| Metro |
0.99 |
1.730 |
0.092 |
0.034 |
48.651 |
| DEMetro_Z |
0.0 |
1.969 |
0.101 |
0.042 |
44.517 |
| DEMetro_Z |
0.3 |
1.466 |
0.108 |
0.051 |
26.599 |
| DEMetro_Z |
0.5 |
1.636 |
0.065 |
0.030 |
51.562 |
| DEMetro_Z |
0.9 |
1.532 |
0.084 |
0.052 |
27.851 |
| DEMetro_Z |
0.99 |
1.966 |
0.092 |
0.034 |
55.657 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
4.047 |
0.00191 |
31.850 |
| HMC |
0.3 |
4.711 |
0.000634 |
38.778 |
| HMC |
0.5 |
2.227 |
0.0478 |
31.111 |
| HMC |
0.9 |
4.129 |
0.00166 |
28.430 |
| HMC |
0.99 |
2.969 |
0.0128 |
47.993 |
| SMC |
0.0 |
-0.215 |
0.832 |
-0.088 |
| SMC |
0.3 |
1.120 |
0.276 |
0.529 |
| SMC |
0.5 |
0.494 |
0.627 |
0.170 |
| SMC |
0.9 |
0.521 |
0.608 |
0.221 |
| SMC |
0.99 |
0.551 |
0.588 |
0.333 |
| Metro |
0.0 |
3.488 |
0.00506 |
28.224 |
| Metro |
0.3 |
4.055 |
0.00189 |
30.411 |
| Metro |
0.5 |
2.854 |
0.0157 |
30.730 |
| Metro |
0.9 |
4.425 |
0.00101 |
28.553 |
| Metro |
0.99 |
3.844 |
0.00273 |
59.608 |
| DEMetro_Z |
0.0 |
4.696 |
0.00065 |
38.847 |
| DEMetro_Z |
0.3 |
5.006 |
0.000393 |
29.295 |
| DEMetro_Z |
0.5 |
3.721 |
0.00337 |
56.487 |
| DEMetro_Z |
0.9 |
4.168 |
0.00155 |
27.674 |
| DEMetro_Z |
0.99 |
4.015 |
0.00203 |
66.484 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0.0
|
4.674
|
0.000678
|
1.349
|
| DEMetro_Z_vs_SMC |
0.3
|
4.895
|
0.000476
|
1.413
|
| DEMetro_Z_vs_SMC |
0.5
|
3.694
|
0.00354
|
1.066
|
| DEMetro_Z_vs_SMC |
0.9
|
4.144
|
0.00163
|
1.196
|
| DEMetro_Z_vs_SMC |
0.99
|
4.003
|
0.00207
|
1.156
|
| HMC_vs_Metro |
0.0
|
0.924
|
0.375
|
0.267
|
| HMC_vs_Metro |
0.3
|
0.944
|
0.365
|
0.273
|
| HMC_vs_Metro |
0.5
|
0.019
|
0.985
|
0.006
|
| HMC_vs_Metro |
0.9
|
-0.019
|
0.985
|
-0.005
|
| HMC_vs_Metro |
0.99
|
-0.453
|
0.659
|
-0.131
|
| Metro_vs_DEMetro_Z |
0.0
|
-0.879
|
0.398
|
-0.254
|
| Metro_vs_DEMetro_Z |
0.3
|
0.104
|
0.919
|
0.030
|
| Metro_vs_DEMetro_Z |
0.5
|
-1.280
|
0.227
|
-0.369
|
| Metro_vs_DEMetro_Z |
0.9
|
0.099
|
0.923
|
0.029
|
| Metro_vs_DEMetro_Z |
0.99
|
-0.353
|
0.731
|
-0.102
|
| HMC_vs_SMC |
0.0
|
4.083
|
0.00181
|
1.179
|
| HMC_vs_SMC |
0.3
|
4.776
|
0.000575
|
1.379
|
| HMC_vs_SMC |
0.5
|
2.196
|
0.0504
|
0.634
|
| HMC_vs_SMC |
0.9
|
4.048
|
0.00192
|
1.169
|
| HMC_vs_SMC |
0.99
|
2.961
|
0.0129
|
0.855
|
| Metro_vs_SMC |
0.0
|
3.521
|
0.00479
|
1.016
|
| Metro_vs_SMC |
0.3
|
4.075
|
0.00184
|
1.176
|
| Metro_vs_SMC |
0.5
|
2.853
|
0.0157
|
0.824
|
| Metro_vs_SMC |
0.9
|
4.285
|
0.00129
|
1.237
|
| Metro_vs_SMC |
0.99
|
3.741
|
0.00326
|
1.080
|
| HMC_vs_DEMetro_Z |
0.0
|
-0.538
|
0.601
|
-0.155
|
| HMC_vs_DEMetro_Z |
0.3
|
0.857
|
0.41
|
0.247
|
| HMC_vs_DEMetro_Z |
0.5
|
-1.443
|
0.177
|
-0.416
|
| HMC_vs_DEMetro_Z |
0.9
|
0.080
|
0.938
|
0.023
|
| HMC_vs_DEMetro_Z |
0.99
|
-0.848
|
0.415
|
-0.245
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.246 |
0.013 |
0.007 |
31.850 |
| HMC |
0.3 |
0.293 |
0.014 |
0.007 |
38.778 |
| HMC |
0.5 |
0.141 |
0.007 |
0.004 |
31.111 |
| HMC |
0.9 |
0.251 |
0.010 |
0.008 |
28.430 |
| HMC |
0.99 |
0.218 |
0.011 |
0.004 |
47.993 |
| SMC |
0.0 |
0.013 |
0.013 |
0.007 |
-0.088 |
| SMC |
0.3 |
0.017 |
0.014 |
0.007 |
0.529 |
| SMC |
0.5 |
0.008 |
0.007 |
0.004 |
0.170 |
| SMC |
0.9 |
0.012 |
0.010 |
0.008 |
0.221 |
| SMC |
0.99 |
0.012 |
0.011 |
0.004 |
0.333 |
| Metro |
0.0 |
0.220 |
0.013 |
0.007 |
28.224 |
| Metro |
0.3 |
0.233 |
0.014 |
0.007 |
30.411 |
| Metro |
0.5 |
0.139 |
0.007 |
0.004 |
30.730 |
| Metro |
0.9 |
0.252 |
0.010 |
0.008 |
28.553 |
| Metro |
0.99 |
0.269 |
0.011 |
0.004 |
59.608 |
| DEMetro_Z |
0.0 |
0.297 |
0.013 |
0.007 |
38.847 |
| DEMetro_Z |
0.3 |
0.225 |
0.014 |
0.007 |
29.295 |
| DEMetro_Z |
0.5 |
0.250 |
0.007 |
0.004 |
56.487 |
| DEMetro_Z |
0.9 |
0.245 |
0.010 |
0.008 |
27.674 |
| DEMetro_Z |
0.99 |
0.298 |
0.011 |
0.004 |
66.484 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
R Hat (scatter)
Mode Transitions
One Chain results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
172.154 |
6.01e-34 |
82.016 |
| HMC |
0.3 |
141.550 |
1.91e-29 |
77.236 |
| HMC |
0.5 |
207.636 |
4.2e-32 |
115.379 |
| HMC |
0.9 |
162.269 |
3.94e-34 |
74.489 |
| HMC |
0.99 |
179.000 |
5.49e-28 |
116.364 |
| SMC |
0.0 |
0.188 |
0.853 |
0.082 |
| SMC |
0.3 |
0.356 |
0.726 |
0.166 |
| SMC |
0.5 |
1.638 |
0.117 |
0.776 |
| SMC |
0.9 |
1.219 |
0.236 |
0.484 |
| SMC |
0.99 |
0.424 |
0.676 |
0.221 |
| Metro |
0.0 |
167.950 |
3.53e-33 |
82.138 |
| Metro |
0.3 |
147.417 |
2e-30 |
77.908 |
| Metro |
0.5 |
188.391 |
2.1e-29 |
115.277 |
| Metro |
0.9 |
137.567 |
2.99e-29 |
74.934 |
| Metro |
0.99 |
54.838 |
3.34e-15 |
114.334 |
| DEMetro_Z |
0.0 |
8.442 |
3.84e-06 |
69.852 |
| DEMetro_Z |
0.3 |
5.246 |
0.000273 |
53.742 |
| DEMetro_Z |
0.5 |
8.651 |
3.05e-06 |
99.645 |
| DEMetro_Z |
0.9 |
13.002 |
4.77e-08 |
69.092 |
| DEMetro_Z |
0.99 |
182.558 |
2.23e-28 |
116.874 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0.0
|
1.467
|
0.17
|
0.424
|
| HMC_vs_DEMetro_Z |
0.3
|
2.361
|
0.0377
|
0.682
|
| HMC_vs_DEMetro_Z |
0.5
|
1.391
|
0.192
|
0.402
|
| HMC_vs_DEMetro_Z |
0.9
|
1.016
|
0.331
|
0.293
|
| HMC_vs_DEMetro_Z |
0.99
|
-0.597
|
0.563
|
-0.172
|
| Metro_vs_SMC |
0.0
|
153.819
|
1.1e-19
|
44.404
|
| Metro_vs_SMC |
0.3
|
143.411
|
2.37e-19
|
41.399
|
| Metro_vs_SMC |
0.5
|
138.373
|
3.52e-19
|
39.945
|
| Metro_vs_SMC |
0.9
|
155.230
|
9.94e-20
|
44.811
|
| Metro_vs_SMC |
0.99
|
56.387
|
6.74e-15
|
16.278
|
| Metro_vs_DEMetro_Z |
0.0
|
1.472
|
0.169
|
0.425
|
| Metro_vs_DEMetro_Z |
0.3
|
2.307
|
0.0415
|
0.666
|
| Metro_vs_DEMetro_Z |
0.5
|
1.388
|
0.193
|
0.401
|
| Metro_vs_DEMetro_Z |
0.9
|
1.098
|
0.296
|
0.317
|
| Metro_vs_DEMetro_Z |
0.99
|
-1.496
|
0.163
|
-0.432
|
| HMC_vs_Metro |
0.0
|
-0.762
|
0.462
|
-0.220
|
| HMC_vs_Metro |
0.3
|
-0.900
|
0.387
|
-0.260
|
| HMC_vs_Metro |
0.5
|
0.400
|
0.697
|
0.116
|
| HMC_vs_Metro |
0.9
|
-0.811
|
0.435
|
-0.234
|
| HMC_vs_Metro |
0.99
|
1.061
|
0.311
|
0.306
|
| HMC_vs_SMC |
0.0
|
154.356
|
1.06e-19
|
44.559
|
| HMC_vs_SMC |
0.3
|
104.587
|
7.63e-18
|
30.192
|
| HMC_vs_SMC |
0.5
|
147.331
|
1.76e-19
|
42.531
|
| HMC_vs_SMC |
0.9
|
156.112
|
9.34e-20
|
45.066
|
| HMC_vs_SMC |
0.99
|
167.606
|
4.28e-20
|
48.384
|
| DEMetro_Z_vs_SMC |
0.0
|
8.419
|
4.01e-06
|
2.430
|
| DEMetro_Z_vs_SMC |
0.3
|
5.218
|
0.000287
|
1.506
|
| DEMetro_Z_vs_SMC |
0.5
|
8.420
|
4e-06
|
2.431
|
| DEMetro_Z_vs_SMC |
0.9
|
12.927
|
5.39e-08
|
3.732
|
| DEMetro_Z_vs_SMC |
0.99
|
153.290
|
1.14e-19
|
44.251
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
4.596 |
0.092 |
0.055 |
82.016 |
| HMC |
0.3 |
4.587 |
0.101 |
0.058 |
77.236 |
| HMC |
0.5 |
4.577 |
0.046 |
0.039 |
115.379 |
| HMC |
0.9 |
4.598 |
0.074 |
0.061 |
74.489 |
| HMC |
0.99 |
4.585 |
0.079 |
0.039 |
116.364 |
| SMC |
0.0 |
0.097 |
0.092 |
0.055 |
0.082 |
| SMC |
0.3 |
0.111 |
0.101 |
0.058 |
0.166 |
| SMC |
0.5 |
0.077 |
0.046 |
0.039 |
0.776 |
| SMC |
0.9 |
0.103 |
0.074 |
0.061 |
0.484 |
| SMC |
0.99 |
0.087 |
0.079 |
0.039 |
0.221 |
| Metro |
0.0 |
4.603 |
0.092 |
0.055 |
82.138 |
| Metro |
0.3 |
4.626 |
0.101 |
0.058 |
77.908 |
| Metro |
0.5 |
4.573 |
0.046 |
0.039 |
115.277 |
| Metro |
0.9 |
4.625 |
0.074 |
0.061 |
74.934 |
| Metro |
0.99 |
4.507 |
0.079 |
0.039 |
114.334 |
| DEMetro_Z |
0.0 |
3.928 |
0.092 |
0.055 |
69.852 |
| DEMetro_Z |
0.3 |
3.222 |
0.101 |
0.058 |
53.742 |
| DEMetro_Z |
0.5 |
3.959 |
0.046 |
0.039 |
99.645 |
| DEMetro_Z |
0.9 |
4.270 |
0.074 |
0.061 |
69.092 |
| DEMetro_Z |
0.99 |
4.605 |
0.079 |
0.039 |
116.874 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
460.440 |
5.08e-44 |
208.235 |
| HMC |
0.3 |
544.910 |
8.97e-47 |
215.797 |
| HMC |
0.5 |
533.268 |
6.41e-37 |
327.448 |
| HMC |
0.9 |
563.109 |
1.87e-39 |
318.667 |
| HMC |
0.99 |
560.081 |
1.39e-46 |
244.148 |
| SMC |
0.0 |
-0.199 |
0.844 |
-0.071 |
| SMC |
0.3 |
0.880 |
0.389 |
0.314 |
| SMC |
0.5 |
0.695 |
0.497 |
0.447 |
| SMC |
0.9 |
2.578 |
0.0194 |
1.528 |
| SMC |
0.99 |
-1.636 |
0.118 |
-0.567 |
| Metro |
0.0 |
451.464 |
2.22e-43 |
208.230 |
| Metro |
0.3 |
514.118 |
2.94e-46 |
215.852 |
| Metro |
0.5 |
492.084 |
1.45e-34 |
327.549 |
| Metro |
0.9 |
622.830 |
2.9e-43 |
318.635 |
| Metro |
0.99 |
354.135 |
1.38e-31 |
245.318 |
| DEMetro_Z |
0.0 |
7.416 |
1.33e-05 |
173.648 |
| DEMetro_Z |
0.3 |
4.769 |
0.000581 |
144.556 |
| DEMetro_Z |
0.5 |
7.466 |
1.25e-05 |
273.016 |
| DEMetro_Z |
0.9 |
11.133 |
2.5e-07 |
292.740 |
| DEMetro_Z |
0.99 |
570.382 |
4.84e-47 |
244.033 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0.0
|
437.137
|
1.13e-24
|
126.191
|
| HMC_vs_SMC |
0.3
|
582.634
|
4.78e-26
|
168.192
|
| HMC_vs_SMC |
0.5
|
444.121
|
9.47e-25
|
128.207
|
| HMC_vs_SMC |
0.9
|
473.474
|
4.68e-25
|
136.680
|
| HMC_vs_SMC |
0.99
|
549.683
|
9.07e-26
|
158.680
|
| Metro_vs_DEMetro_Z |
0.0
|
1.488
|
0.165
|
0.430
|
| Metro_vs_DEMetro_Z |
0.3
|
2.348
|
0.0386
|
0.678
|
| Metro_vs_DEMetro_Z |
0.5
|
1.481
|
0.167
|
0.427
|
| Metro_vs_DEMetro_Z |
0.9
|
0.986
|
0.345
|
0.285
|
| Metro_vs_DEMetro_Z |
0.99
|
2.166
|
0.0531
|
0.625
|
| HMC_vs_Metro |
0.0
|
0.044
|
0.966
|
0.013
|
| HMC_vs_Metro |
0.3
|
-0.713
|
0.491
|
-0.206
|
| HMC_vs_Metro |
0.5
|
-0.544
|
0.597
|
-0.157
|
| HMC_vs_Metro |
0.9
|
0.113
|
0.912
|
0.033
|
| HMC_vs_Metro |
0.99
|
-2.027
|
0.0676
|
-0.585
|
| HMC_vs_DEMetro_Z |
0.0
|
1.488
|
0.165
|
0.430
|
| HMC_vs_DEMetro_Z |
0.3
|
2.350
|
0.0385
|
0.678
|
| HMC_vs_DEMetro_Z |
0.5
|
1.479
|
0.167
|
0.427
|
| HMC_vs_DEMetro_Z |
0.9
|
0.990
|
0.344
|
0.286
|
| HMC_vs_DEMetro_Z |
0.99
|
0.854
|
0.411
|
0.247
|
| Metro_vs_SMC |
0.0
|
423.613
|
1.59e-24
|
122.287
|
| Metro_vs_SMC |
0.3
|
553.142
|
8.47e-26
|
159.678
|
| Metro_vs_SMC |
0.5
|
421.813
|
1.67e-24
|
121.767
|
| Metro_vs_SMC |
0.9
|
457.108
|
6.9e-25
|
131.956
|
| Metro_vs_SMC |
0.99
|
403.537
|
2.72e-24
|
116.491
|
| DEMetro_Z_vs_SMC |
0.0
|
7.367
|
1.42e-05
|
2.127
|
| DEMetro_Z_vs_SMC |
0.3
|
4.769
|
0.000582
|
1.377
|
| DEMetro_Z_vs_SMC |
0.5
|
7.421
|
1.32e-05
|
2.142
|
| DEMetro_Z_vs_SMC |
0.9
|
11.111
|
2.55e-07
|
3.208
|
| DEMetro_Z_vs_SMC |
0.99
|
555.370
|
8.1e-26
|
160.321
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
29.869 |
0.187 |
0.143 |
208.235 |
| HMC |
0.3 |
29.810 |
0.190 |
0.137 |
215.797 |
| HMC |
0.5 |
29.864 |
0.144 |
0.091 |
327.448 |
| HMC |
0.9 |
29.866 |
0.111 |
0.093 |
318.667 |
| HMC |
0.99 |
29.886 |
0.199 |
0.122 |
244.148 |
| SMC |
0.0 |
0.176 |
0.187 |
0.143 |
-0.071 |
| SMC |
0.3 |
0.233 |
0.190 |
0.137 |
0.314 |
| SMC |
0.5 |
0.184 |
0.144 |
0.091 |
0.447 |
| SMC |
0.9 |
0.254 |
0.111 |
0.093 |
1.528 |
| SMC |
0.99 |
0.130 |
0.199 |
0.122 |
-0.567 |
| Metro |
0.0 |
29.868 |
0.187 |
0.143 |
208.230 |
| Metro |
0.3 |
29.818 |
0.190 |
0.137 |
215.852 |
| Metro |
0.5 |
29.873 |
0.144 |
0.091 |
327.549 |
| Metro |
0.9 |
29.863 |
0.111 |
0.093 |
318.635 |
| Metro |
0.99 |
30.028 |
0.199 |
0.122 |
245.318 |
| DEMetro_Z |
0.0 |
24.939 |
0.187 |
0.143 |
173.648 |
| DEMetro_Z |
0.3 |
20.032 |
0.190 |
0.137 |
144.556 |
| DEMetro_Z |
0.5 |
24.923 |
0.144 |
0.091 |
273.016 |
| DEMetro_Z |
0.9 |
27.445 |
0.111 |
0.093 |
292.740 |
| DEMetro_Z |
0.99 |
29.872 |
0.199 |
0.122 |
244.033 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
53.525 |
2.99e-15 |
94.972 |
| HMC |
0.3 |
55.130 |
9.11e-16 |
77.645 |
| HMC |
0.5 |
55.015 |
4.08e-15 |
130.828 |
| HMC |
0.9 |
41.815 |
5.52e-14 |
76.214 |
| HMC |
0.99 |
55.693 |
3.11e-15 |
122.474 |
| SMC |
0.0 |
0.236 |
0.816 |
0.109 |
| SMC |
0.3 |
0.524 |
0.606 |
0.249 |
| SMC |
0.5 |
1.699 |
0.105 |
0.835 |
| SMC |
0.9 |
1.290 |
0.211 |
0.531 |
| SMC |
0.99 |
0.153 |
0.88 |
0.072 |
| Metro |
0.0 |
53.249 |
3.46e-15 |
97.462 |
| Metro |
0.3 |
57.314 |
5.19e-16 |
79.086 |
| Metro |
0.5 |
45.481 |
4.42e-14 |
132.220 |
| Metro |
0.9 |
50.878 |
3.65e-15 |
79.824 |
| Metro |
0.99 |
44.584 |
5.22e-14 |
122.527 |
| DEMetro_Z |
0.0 |
8.388 |
4.1e-06 |
80.001 |
| DEMetro_Z |
0.3 |
5.249 |
0.000271 |
52.526 |
| DEMetro_Z |
0.5 |
8.417 |
3.99e-06 |
115.485 |
| DEMetro_Z |
0.9 |
12.665 |
6.32e-08 |
71.226 |
| DEMetro_Z |
0.99 |
66.802 |
2.67e-16 |
124.541 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0.0
|
1.759
|
0.106
|
0.508
|
| Metro_vs_DEMetro_Z |
0.3
|
2.563
|
0.0264
|
0.740
|
| Metro_vs_DEMetro_Z |
0.5
|
1.292
|
0.223
|
0.373
|
| Metro_vs_DEMetro_Z |
0.9
|
1.856
|
0.0904
|
0.536
|
| Metro_vs_DEMetro_Z |
0.99
|
-0.626
|
0.544
|
-0.181
|
| DEMetro_Z_vs_SMC |
0.0
|
8.383
|
4.18e-06
|
2.420
|
| DEMetro_Z_vs_SMC |
0.3
|
5.221
|
0.000285
|
1.507
|
| DEMetro_Z_vs_SMC |
0.5
|
8.189
|
5.23e-06
|
2.364
|
| DEMetro_Z_vs_SMC |
0.9
|
12.689
|
6.54e-08
|
3.663
|
| DEMetro_Z_vs_SMC |
0.99
|
75.423
|
2.77e-16
|
21.773
|
| HMC_vs_DEMetro_Z |
0.0
|
1.766
|
0.105
|
0.510
|
| HMC_vs_DEMetro_Z |
0.3
|
2.574
|
0.0259
|
0.743
|
| HMC_vs_DEMetro_Z |
0.5
|
1.196
|
0.257
|
0.345
|
| HMC_vs_DEMetro_Z |
0.9
|
0.910
|
0.382
|
0.263
|
| HMC_vs_DEMetro_Z |
0.99
|
-0.737
|
0.476
|
-0.213
|
| HMC_vs_Metro |
0.0
|
-0.966
|
0.355
|
-0.279
|
| HMC_vs_Metro |
0.3
|
-0.948
|
0.363
|
-0.274
|
| HMC_vs_Metro |
0.5
|
-0.397
|
0.699
|
-0.114
|
| HMC_vs_Metro |
0.9
|
-1.472
|
0.169
|
-0.425
|
| HMC_vs_Metro |
0.99
|
-0.015
|
0.988
|
-0.004
|
| HMC_vs_SMC |
0.0
|
52.832
|
1.38e-14
|
15.251
|
| HMC_vs_SMC |
0.3
|
51.770
|
1.72e-14
|
14.945
|
| HMC_vs_SMC |
0.5
|
49.518
|
2.8e-14
|
14.295
|
| HMC_vs_SMC |
0.9
|
40.670
|
2.41e-13
|
11.740
|
| HMC_vs_SMC |
0.99
|
54.724
|
9.35e-15
|
15.797
|
| Metro_vs_SMC |
0.0
|
55.221
|
8.47e-15
|
15.941
|
| Metro_vs_SMC |
0.3
|
55.263
|
8.4e-15
|
15.953
|
| Metro_vs_SMC |
0.5
|
41.852
|
1.76e-13
|
12.082
|
| Metro_vs_SMC |
0.9
|
53.878
|
1.11e-14
|
15.553
|
| Metro_vs_SMC |
0.99
|
44.366
|
9.32e-14
|
12.807
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
4.087 |
0.101 |
0.042 |
94.972 |
| HMC |
0.3 |
4.072 |
0.108 |
0.051 |
77.645 |
| HMC |
0.5 |
4.051 |
0.065 |
0.030 |
130.828 |
| HMC |
0.9 |
4.047 |
0.084 |
0.052 |
76.214 |
| HMC |
0.99 |
4.217 |
0.092 |
0.034 |
122.474 |
| SMC |
0.0 |
0.105 |
0.101 |
0.042 |
0.109 |
| SMC |
0.3 |
0.120 |
0.108 |
0.051 |
0.249 |
| SMC |
0.5 |
0.090 |
0.065 |
0.030 |
0.835 |
| SMC |
0.9 |
0.111 |
0.084 |
0.052 |
0.531 |
| SMC |
0.99 |
0.094 |
0.092 |
0.034 |
0.072 |
| Metro |
0.0 |
4.192 |
0.101 |
0.042 |
97.462 |
| Metro |
0.3 |
4.146 |
0.108 |
0.051 |
79.086 |
| Metro |
0.5 |
4.093 |
0.065 |
0.030 |
132.220 |
| Metro |
0.9 |
4.235 |
0.084 |
0.052 |
79.824 |
| Metro |
0.99 |
4.219 |
0.092 |
0.034 |
122.527 |
| DEMetro_Z |
0.0 |
3.459 |
0.101 |
0.042 |
80.001 |
| DEMetro_Z |
0.3 |
2.790 |
0.108 |
0.051 |
52.526 |
| DEMetro_Z |
0.5 |
3.583 |
0.065 |
0.030 |
115.485 |
| DEMetro_Z |
0.9 |
3.787 |
0.084 |
0.052 |
71.226 |
| DEMetro_Z |
0.99 |
4.287 |
0.092 |
0.034 |
124.541 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
116.322 |
6.56e-24 |
82.057 |
| HMC |
0.3 |
116.564 |
1.27e-23 |
84.366 |
| HMC |
0.5 |
134.514 |
1.32e-21 |
139.327 |
| HMC |
0.9 |
110.426 |
1.57e-24 |
72.216 |
| HMC |
0.99 |
95.055 |
1.85e-18 |
141.698 |
| SMC |
0.0 |
0.207 |
0.838 |
0.096 |
| SMC |
0.3 |
0.443 |
0.662 |
0.198 |
| SMC |
0.5 |
1.953 |
0.066 |
1.059 |
| SMC |
0.9 |
1.004 |
0.327 |
0.371 |
| SMC |
0.99 |
0.373 |
0.714 |
0.214 |
| Metro |
0.0 |
115.377 |
1.04e-23 |
82.409 |
| Metro |
0.3 |
96.318 |
1.05e-20 |
84.597 |
| Metro |
0.5 |
98.817 |
8.86e-19 |
139.932 |
| Metro |
0.9 |
95.881 |
6.58e-22 |
72.508 |
| Metro |
0.99 |
65.647 |
5.14e-16 |
149.623 |
| DEMetro_Z |
0.0 |
8.481 |
3.67e-06 |
70.982 |
| DEMetro_Z |
0.3 |
5.433 |
0.000205 |
58.667 |
| DEMetro_Z |
0.5 |
8.740 |
2.77e-06 |
121.358 |
| DEMetro_Z |
0.9 |
13.132 |
4.27e-08 |
66.776 |
| DEMetro_Z |
0.99 |
95.901 |
1.72e-18 |
143.740 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0.0
|
8.494
|
3.68e-06
|
2.452
|
| DEMetro_Z_vs_SMC |
0.3
|
5.411
|
0.000213
|
1.562
|
| DEMetro_Z_vs_SMC |
0.5
|
8.456
|
3.84e-06
|
2.441
|
| DEMetro_Z_vs_SMC |
0.9
|
13.099
|
4.7e-08
|
3.781
|
| DEMetro_Z_vs_SMC |
0.99
|
90.892
|
3.57e-17
|
26.238
|
| HMC_vs_Metro |
0.0
|
-0.438
|
0.67
|
-0.126
|
| HMC_vs_Metro |
0.3
|
-0.191
|
0.852
|
-0.055
|
| HMC_vs_Metro |
0.5
|
-0.301
|
0.769
|
-0.087
|
| HMC_vs_Metro |
0.9
|
-0.287
|
0.779
|
-0.083
|
| HMC_vs_Metro |
0.99
|
-2.824
|
0.0165
|
-0.815
|
| Metro_vs_DEMetro_Z |
0.0
|
1.320
|
0.214
|
0.381
|
| Metro_vs_DEMetro_Z |
0.3
|
2.364
|
0.0375
|
0.683
|
| Metro_vs_DEMetro_Z |
0.5
|
1.379
|
0.195
|
0.398
|
| Metro_vs_DEMetro_Z |
0.9
|
1.072
|
0.307
|
0.309
|
| Metro_vs_DEMetro_Z |
0.99
|
1.860
|
0.0898
|
0.537
|
| HMC_vs_SMC |
0.0
|
103.040
|
8.99e-18
|
29.745
|
| HMC_vs_SMC |
0.3
|
102.233
|
9.8e-18
|
29.512
|
| HMC_vs_SMC |
0.5
|
142.496
|
2.55e-19
|
41.135
|
| HMC_vs_SMC |
0.9
|
102.398
|
9.63e-18
|
29.560
|
| HMC_vs_SMC |
0.99
|
98.779
|
1.43e-17
|
28.515
|
| Metro_vs_SMC |
0.0
|
98.677
|
1.45e-17
|
28.486
|
| Metro_vs_SMC |
0.3
|
84.387
|
8.07e-17
|
24.360
|
| Metro_vs_SMC |
0.5
|
81.188
|
1.23e-16
|
23.437
|
| Metro_vs_SMC |
0.9
|
92.252
|
3.03e-17
|
26.631
|
| Metro_vs_SMC |
0.99
|
69.074
|
7.27e-16
|
19.940
|
| HMC_vs_DEMetro_Z |
0.0
|
1.283
|
0.226
|
0.370
|
| HMC_vs_DEMetro_Z |
0.3
|
2.496
|
0.0297
|
0.720
|
| HMC_vs_DEMetro_Z |
0.5
|
1.298
|
0.221
|
0.375
|
| HMC_vs_DEMetro_Z |
0.9
|
1.121
|
0.286
|
0.324
|
| HMC_vs_DEMetro_Z |
0.99
|
-0.828
|
0.425
|
-0.239
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.614 |
0.013 |
0.007 |
82.057 |
| HMC |
0.3 |
0.623 |
0.014 |
0.007 |
84.366 |
| HMC |
0.5 |
0.606 |
0.007 |
0.004 |
139.327 |
| HMC |
0.9 |
0.623 |
0.010 |
0.008 |
72.216 |
| HMC |
0.99 |
0.624 |
0.011 |
0.004 |
141.698 |
| SMC |
0.0 |
0.014 |
0.013 |
0.007 |
0.096 |
| SMC |
0.3 |
0.015 |
0.014 |
0.007 |
0.198 |
| SMC |
0.5 |
0.012 |
0.007 |
0.004 |
1.059 |
| SMC |
0.9 |
0.014 |
0.010 |
0.008 |
0.371 |
| SMC |
0.99 |
0.011 |
0.011 |
0.004 |
0.214 |
| Metro |
0.0 |
0.616 |
0.013 |
0.007 |
82.409 |
| Metro |
0.3 |
0.624 |
0.014 |
0.007 |
84.597 |
| Metro |
0.5 |
0.609 |
0.007 |
0.004 |
139.932 |
| Metro |
0.9 |
0.625 |
0.010 |
0.008 |
72.508 |
| Metro |
0.99 |
0.658 |
0.011 |
0.004 |
149.623 |
| DEMetro_Z |
0.0 |
0.533 |
0.013 |
0.007 |
70.982 |
| DEMetro_Z |
0.3 |
0.437 |
0.014 |
0.007 |
58.667 |
| DEMetro_Z |
0.5 |
0.529 |
0.007 |
0.004 |
121.358 |
| DEMetro_Z |
0.9 |
0.576 |
0.010 |
0.008 |
66.776 |
| DEMetro_Z |
0.99 |
0.633 |
0.011 |
0.004 |
143.740 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
Mode Transitions
Mode Transitions (scatter)
KDE + Init Plots
Forest & Ridge Plots
Pooled
Chain
Pairwise Scatter Plots
Pooled
Chain
Vary_Dimension_with_high_correlation
(MvNormal,
dimension,
12 runs)
Pooled Chains results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
0.063 |
0.95 |
0.028 |
| HMC |
5 |
3.864 |
0.00172 |
3.196 |
| HMC |
10 |
3.629 |
0.0019 |
2.013 |
| HMC |
15 |
2.861 |
0.0114 |
1.891 |
| HMC |
30 |
3.407 |
0.00519 |
4.652 |
| SMC |
2 |
-3.579 |
0.00238 |
-1.167 |
| SMC |
5 |
0.820 |
0.421 |
0.343 |
| SMC |
10 |
-0.007 |
0.994 |
-0.003 |
| SMC |
15 |
-0.704 |
0.489 |
-0.299 |
| SMC |
30 |
0.744 |
0.465 |
0.303 |
| Metro |
2 |
3.779 |
0.00274 |
6.182 |
| Metro |
5 |
6.493 |
4.17e-05 |
21.766 |
| Metro |
10 |
4.909 |
0.000444 |
15.768 |
| Metro |
15 |
4.845 |
0.000496 |
17.129 |
| Metro |
30 |
4.375 |
0.00109 |
22.776 |
| DEMetro_Z |
2 |
2.245 |
0.0396 |
1.520 |
| DEMetro_Z |
5 |
6.003 |
8.89e-05 |
788.290 |
| DEMetro_Z |
10 |
13.121 |
4.62e-08 |
499.307 |
| DEMetro_Z |
15 |
13.418 |
3.66e-08 |
486.752 |
| DEMetro_Z |
30 |
25.371 |
4.09e-11 |
594.295 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
-2.698
|
0.0207
|
-0.779
|
| HMC_vs_DEMetro_Z |
1
|
-5.989
|
9.07e-05
|
-1.729
|
| HMC_vs_DEMetro_Z |
2
|
-13.045
|
4.91e-08
|
-3.766
|
| HMC_vs_DEMetro_Z |
3
|
-13.367
|
3.81e-08
|
-3.859
|
| HMC_vs_DEMetro_Z |
4
|
-25.249
|
4.33e-11
|
-7.289
|
| Metro_vs_SMC |
0
|
4.639
|
0.000718
|
1.339
|
| Metro_vs_SMC |
1
|
6.293
|
5.9e-05
|
1.817
|
| Metro_vs_SMC |
2
|
4.964
|
0.000426
|
1.433
|
| Metro_vs_SMC |
3
|
4.998
|
0.000403
|
1.443
|
| Metro_vs_SMC |
4
|
4.350
|
0.00115
|
1.256
|
| Metro_vs_DEMetro_Z |
0
|
3.604
|
0.00414
|
1.040
|
| Metro_vs_DEMetro_Z |
1
|
-5.752
|
0.000128
|
-1.660
|
| Metro_vs_DEMetro_Z |
2
|
-12.605
|
7.01e-08
|
-3.639
|
| Metro_vs_DEMetro_Z |
3
|
-12.828
|
5.84e-08
|
-3.703
|
| Metro_vs_DEMetro_Z |
4
|
-25.850
|
3.36e-11
|
-7.462
|
| HMC_vs_Metro |
0
|
-3.993
|
0.00211
|
-1.153
|
| HMC_vs_Metro |
1
|
-4.983
|
0.000413
|
-1.439
|
| HMC_vs_Metro |
2
|
-4.265
|
0.00133
|
-1.231
|
| HMC_vs_Metro |
3
|
-4.494
|
0.00091
|
-1.297
|
| HMC_vs_Metro |
4
|
-3.520
|
0.0048
|
-1.016
|
| HMC_vs_SMC |
0
|
2.979
|
0.0125
|
0.860
|
| HMC_vs_SMC |
1
|
3.730
|
0.00332
|
1.077
|
| HMC_vs_SMC |
2
|
3.139
|
0.00942
|
0.906
|
| HMC_vs_SMC |
3
|
3.619
|
0.00403
|
1.045
|
| HMC_vs_SMC |
4
|
3.001
|
0.0121
|
0.866
|
| DEMetro_Z_vs_SMC |
0
|
3.957
|
0.00225
|
1.142
|
| DEMetro_Z_vs_SMC |
1
|
5.998
|
8.95e-05
|
1.731
|
| DEMetro_Z_vs_SMC |
2
|
13.132
|
4.58e-08
|
3.791
|
| DEMetro_Z_vs_SMC |
3
|
13.434
|
3.62e-08
|
3.878
|
| DEMetro_Z_vs_SMC |
4
|
25.488
|
3.91e-11
|
7.358
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.028 |
0.028 |
0.014 |
0.028 |
| HMC |
5 |
0.039 |
0.015 |
0.007 |
3.196 |
| HMC |
10 |
0.038 |
0.015 |
0.012 |
2.013 |
| HMC |
15 |
0.046 |
0.024 |
0.012 |
1.891 |
| HMC |
30 |
0.071 |
0.018 |
0.011 |
4.652 |
| SMC |
2 |
0.012 |
0.028 |
0.014 |
-1.167 |
| SMC |
5 |
0.018 |
0.015 |
0.007 |
0.343 |
| SMC |
10 |
0.015 |
0.015 |
0.012 |
-0.003 |
| SMC |
15 |
0.020 |
0.024 |
0.012 |
-0.299 |
| SMC |
30 |
0.022 |
0.018 |
0.011 |
0.303 |
| Metro |
2 |
0.111 |
0.028 |
0.014 |
6.182 |
| Metro |
5 |
0.178 |
0.015 |
0.007 |
21.766 |
| Metro |
10 |
0.196 |
0.015 |
0.012 |
15.768 |
| Metro |
15 |
0.224 |
0.024 |
0.012 |
17.129 |
| Metro |
30 |
0.278 |
0.018 |
0.011 |
22.776 |
| DEMetro_Z |
2 |
0.048 |
0.028 |
0.014 |
1.520 |
| DEMetro_Z |
5 |
5.909 |
0.015 |
0.007 |
788.290 |
| DEMetro_Z |
10 |
5.759 |
0.015 |
0.012 |
499.307 |
| DEMetro_Z |
15 |
5.733 |
0.024 |
0.012 |
486.752 |
| DEMetro_Z |
30 |
6.803 |
0.018 |
0.011 |
594.295 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
3.080 |
0.00658 |
1.781 |
| HMC |
5 |
2.283 |
0.0413 |
3.032 |
| HMC |
10 |
1.449 |
0.164 |
0.798 |
| HMC |
15 |
2.337 |
0.0374 |
3.056 |
| HMC |
30 |
3.589 |
0.00346 |
3.969 |
| SMC |
2 |
1.421 |
0.17 |
0.660 |
| SMC |
5 |
1.347 |
0.195 |
0.747 |
| SMC |
10 |
-0.217 |
0.83 |
-0.089 |
| SMC |
15 |
0.189 |
0.852 |
0.079 |
| SMC |
30 |
-0.553 |
0.587 |
-0.185 |
| Metro |
2 |
5.150 |
0.00027 |
9.292 |
| Metro |
5 |
4.589 |
0.000759 |
18.741 |
| Metro |
10 |
3.457 |
0.00519 |
9.335 |
| Metro |
15 |
5.496 |
0.000174 |
15.615 |
| Metro |
30 |
5.886 |
9.05e-05 |
12.411 |
| DEMetro_Z |
2 |
3.592 |
0.0033 |
3.617 |
| DEMetro_Z |
5 |
6.652 |
3.6e-05 |
11814.735 |
| DEMetro_Z |
10 |
15.026 |
1.12e-08 |
6977.533 |
| DEMetro_Z |
15 |
36.536 |
7.78e-13 |
11280.894 |
| DEMetro_Z |
30 |
32.984 |
2.37e-12 |
9140.934 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
1.771
|
0.104
|
0.511
|
| HMC_vs_SMC |
1
|
1.675
|
0.122
|
0.484
|
| HMC_vs_SMC |
2
|
1.502
|
0.161
|
0.434
|
| HMC_vs_SMC |
3
|
2.693
|
0.0209
|
0.777
|
| HMC_vs_SMC |
4
|
4.033
|
0.00197
|
1.164
|
| Metro_vs_DEMetro_Z |
0
|
2.639
|
0.023
|
0.762
|
| Metro_vs_DEMetro_Z |
1
|
-6.643
|
3.65e-05
|
-1.918
|
| Metro_vs_DEMetro_Z |
2
|
-15.013
|
1.13e-08
|
-4.334
|
| Metro_vs_DEMetro_Z |
3
|
-36.756
|
7.29e-13
|
-10.611
|
| Metro_vs_DEMetro_Z |
4
|
-32.988
|
2.37e-12
|
-9.523
|
| HMC_vs_Metro |
0
|
-4.264
|
0.00133
|
-1.231
|
| HMC_vs_Metro |
1
|
-3.918
|
0.0024
|
-1.131
|
| HMC_vs_Metro |
2
|
-3.125
|
0.00967
|
-0.902
|
| HMC_vs_Metro |
3
|
-4.280
|
0.0013
|
-1.236
|
| HMC_vs_Metro |
4
|
-3.613
|
0.00408
|
-1.043
|
| HMC_vs_DEMetro_Z |
0
|
-1.477
|
0.168
|
-0.426
|
| HMC_vs_DEMetro_Z |
1
|
-6.651
|
3.61e-05
|
-1.920
|
| HMC_vs_DEMetro_Z |
2
|
-15.026
|
1.12e-08
|
-4.338
|
| HMC_vs_DEMetro_Z |
3
|
-36.581
|
7.68e-13
|
-10.560
|
| HMC_vs_DEMetro_Z |
4
|
-32.957
|
2.4e-12
|
-9.514
|
| Metro_vs_SMC |
0
|
4.997
|
0.000404
|
1.443
|
| Metro_vs_SMC |
1
|
4.274
|
0.00131
|
1.234
|
| Metro_vs_SMC |
2
|
3.413
|
0.0058
|
0.985
|
| Metro_vs_SMC |
3
|
5.502
|
0.000186
|
1.588
|
| Metro_vs_SMC |
4
|
6.104
|
7.69e-05
|
1.762
|
| DEMetro_Z_vs_SMC |
0
|
3.434
|
0.00558
|
0.991
|
| DEMetro_Z_vs_SMC |
1
|
6.651
|
3.6e-05
|
1.920
|
| DEMetro_Z_vs_SMC |
2
|
15.027
|
1.12e-08
|
4.338
|
| DEMetro_Z_vs_SMC |
3
|
36.547
|
7.76e-13
|
10.550
|
| DEMetro_Z_vs_SMC |
4
|
32.971
|
2.38e-12
|
9.518
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.034 |
0.017 |
0.009 |
1.781 |
| HMC |
5 |
0.059 |
0.025 |
0.011 |
3.032 |
| HMC |
10 |
0.047 |
0.032 |
0.019 |
0.798 |
| HMC |
15 |
0.059 |
0.024 |
0.011 |
3.056 |
| HMC |
30 |
0.108 |
0.032 |
0.019 |
3.969 |
| SMC |
2 |
0.024 |
0.017 |
0.009 |
0.660 |
| SMC |
5 |
0.034 |
0.025 |
0.011 |
0.747 |
| SMC |
10 |
0.030 |
0.032 |
0.019 |
-0.089 |
| SMC |
15 |
0.025 |
0.024 |
0.011 |
0.079 |
| SMC |
30 |
0.029 |
0.032 |
0.019 |
-0.185 |
| Metro |
2 |
0.106 |
0.017 |
0.009 |
9.292 |
| Metro |
5 |
0.236 |
0.025 |
0.011 |
18.741 |
| Metro |
10 |
0.206 |
0.032 |
0.019 |
9.335 |
| Metro |
15 |
0.202 |
0.024 |
0.011 |
15.615 |
| Metro |
30 |
0.268 |
0.032 |
0.019 |
12.411 |
| DEMetro_Z |
2 |
0.052 |
0.017 |
0.009 |
3.617 |
| DEMetro_Z |
5 |
132.997 |
0.025 |
0.011 |
11814.735 |
| DEMetro_Z |
10 |
130.624 |
0.032 |
0.019 |
6977.533 |
| DEMetro_Z |
15 |
128.779 |
0.024 |
0.011 |
11280.894 |
| DEMetro_Z |
30 |
173.820 |
0.032 |
0.019 |
9140.934 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
0.579 |
0.569 |
0.265 |
| HMC |
5 |
5.441 |
9.98e-05 |
4.922 |
| HMC |
10 |
4.844 |
0.000102 |
2.431 |
| HMC |
15 |
3.951 |
0.00148 |
3.356 |
| HMC |
30 |
4.362 |
0.00103 |
8.955 |
| SMC |
2 |
-3.411 |
0.00309 |
-1.152 |
| SMC |
5 |
1.300 |
0.207 |
0.573 |
| SMC |
10 |
0.271 |
0.789 |
0.110 |
| SMC |
15 |
0.234 |
0.817 |
0.102 |
| SMC |
30 |
1.647 |
0.114 |
0.640 |
| Metro |
2 |
4.682 |
0.000602 |
9.628 |
| Metro |
5 |
8.316 |
4.1e-06 |
28.169 |
| Metro |
10 |
5.227 |
0.000275 |
23.088 |
| Metro |
15 |
6.589 |
3.76e-05 |
28.134 |
| Metro |
30 |
5.459 |
0.000196 |
39.285 |
| DEMetro_Z |
2 |
2.909 |
0.0111 |
2.227 |
| DEMetro_Z |
5 |
14.712 |
1.4e-08 |
1748.594 |
| DEMetro_Z |
10 |
26.026 |
3.12e-11 |
1344.941 |
| DEMetro_Z |
15 |
36.101 |
8.85e-13 |
1363.419 |
| DEMetro_Z |
30 |
49.751 |
2.65e-14 |
1812.153 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
4.098
|
0.00177
|
1.183
|
| Metro_vs_DEMetro_Z |
1
|
-14.348
|
1.82e-08
|
-4.142
|
| Metro_vs_DEMetro_Z |
2
|
-25.610
|
3.71e-11
|
-7.393
|
| Metro_vs_DEMetro_Z |
3
|
-34.707
|
1.36e-12
|
-10.019
|
| Metro_vs_DEMetro_Z |
4
|
-51.334
|
1.89e-14
|
-14.819
|
| DEMetro_Z_vs_SMC |
0
|
5.247
|
0.000274
|
1.515
|
| DEMetro_Z_vs_SMC |
1
|
14.697
|
1.41e-08
|
4.243
|
| DEMetro_Z_vs_SMC |
2
|
26.085
|
3.04e-11
|
7.530
|
| DEMetro_Z_vs_SMC |
3
|
36.122
|
8.81e-13
|
10.428
|
| DEMetro_Z_vs_SMC |
4
|
49.866
|
2.59e-14
|
14.395
|
| HMC_vs_DEMetro_Z |
0
|
-2.489
|
0.0301
|
-0.719
|
| HMC_vs_DEMetro_Z |
1
|
-14.708
|
1.4e-08
|
-4.246
|
| HMC_vs_DEMetro_Z |
2
|
-25.928
|
3.25e-11
|
-7.485
|
| HMC_vs_DEMetro_Z |
3
|
-35.893
|
9.44e-13
|
-10.361
|
| HMC_vs_DEMetro_Z |
4
|
-49.152
|
3.03e-14
|
-14.189
|
| HMC_vs_Metro |
0
|
-4.688
|
0.000663
|
-1.353
|
| HMC_vs_Metro |
1
|
-6.483
|
4.53e-05
|
-1.871
|
| HMC_vs_Metro |
2
|
-4.586
|
0.000782
|
-1.324
|
| HMC_vs_Metro |
3
|
-6.001
|
8.91e-05
|
-1.732
|
| HMC_vs_Metro |
4
|
-4.069
|
0.00185
|
-1.175
|
| HMC_vs_SMC |
0
|
4.071
|
0.00185
|
1.175
|
| HMC_vs_SMC |
1
|
4.665
|
0.000688
|
1.347
|
| HMC_vs_SMC |
2
|
4.740
|
0.000609
|
1.368
|
| HMC_vs_SMC |
3
|
4.130
|
0.00167
|
1.192
|
| HMC_vs_SMC |
4
|
3.901
|
0.00247
|
1.126
|
| Metro_vs_SMC |
0
|
5.524
|
0.00018
|
1.595
|
| Metro_vs_SMC |
1
|
8.198
|
5.17e-06
|
2.367
|
| Metro_vs_SMC |
2
|
5.163
|
0.000312
|
1.490
|
| Metro_vs_SMC |
3
|
6.574
|
4e-05
|
1.898
|
| Metro_vs_SMC |
4
|
5.374
|
0.000225
|
1.551
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.036 |
0.033 |
0.009 |
0.265 |
| HMC |
5 |
0.047 |
0.022 |
0.005 |
4.922 |
| HMC |
10 |
0.040 |
0.023 |
0.007 |
2.431 |
| HMC |
15 |
0.047 |
0.025 |
0.007 |
3.356 |
| HMC |
30 |
0.076 |
0.024 |
0.006 |
8.955 |
| SMC |
2 |
0.023 |
0.033 |
0.009 |
-1.152 |
| SMC |
5 |
0.025 |
0.022 |
0.005 |
0.573 |
| SMC |
10 |
0.024 |
0.023 |
0.007 |
0.110 |
| SMC |
15 |
0.026 |
0.025 |
0.007 |
0.102 |
| SMC |
30 |
0.027 |
0.024 |
0.006 |
0.640 |
| Metro |
2 |
0.118 |
0.033 |
0.009 |
9.628 |
| Metro |
5 |
0.162 |
0.022 |
0.005 |
28.169 |
| Metro |
10 |
0.179 |
0.023 |
0.007 |
23.088 |
| Metro |
15 |
0.210 |
0.025 |
0.007 |
28.134 |
| Metro |
30 |
0.251 |
0.024 |
0.006 |
39.285 |
| DEMetro_Z |
2 |
0.053 |
0.033 |
0.009 |
2.227 |
| DEMetro_Z |
5 |
8.707 |
0.022 |
0.005 |
1748.594 |
| DEMetro_Z |
10 |
9.095 |
0.023 |
0.007 |
1344.941 |
| DEMetro_Z |
15 |
8.973 |
0.025 |
0.007 |
1363.419 |
| DEMetro_Z |
30 |
10.516 |
0.024 |
0.006 |
1812.153 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
0.972 |
0.345 |
0.586 |
| HMC |
5 |
4.856 |
0.000291 |
4.487 |
| HMC |
10 |
3.789 |
0.0011 |
1.794 |
| HMC |
15 |
3.969 |
0.00129 |
3.002 |
| HMC |
30 |
4.254 |
0.00118 |
7.022 |
| SMC |
2 |
-3.023 |
0.00647 |
-1.120 |
| SMC |
5 |
1.876 |
0.0745 |
0.851 |
| SMC |
10 |
-0.269 |
0.79 |
-0.099 |
| SMC |
15 |
0.431 |
0.671 |
0.159 |
| SMC |
30 |
1.721 |
0.0997 |
0.652 |
| Metro |
2 |
5.141 |
0.00028 |
9.983 |
| Metro |
5 |
7.500 |
1.06e-05 |
20.948 |
| Metro |
10 |
4.884 |
0.00047 |
19.642 |
| Metro |
15 |
8.381 |
3.48e-06 |
20.680 |
| Metro |
30 |
5.879 |
0.000103 |
28.023 |
| DEMetro_Z |
2 |
2.983 |
0.0105 |
2.895 |
| DEMetro_Z |
5 |
42.389 |
1.23e-13 |
176.970 |
| DEMetro_Z |
10 |
29.628 |
6.17e-12 |
114.880 |
| DEMetro_Z |
15 |
30.613 |
4.14e-12 |
109.167 |
| DEMetro_Z |
30 |
50.547 |
1.06e-14 |
120.362 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
5.316
|
0.000246
|
1.535
|
| DEMetro_Z_vs_SMC |
1
|
43.310
|
1.21e-13
|
12.502
|
| DEMetro_Z_vs_SMC |
2
|
30.111
|
6.4e-12
|
8.692
|
| DEMetro_Z_vs_SMC |
3
|
30.154
|
6.31e-12
|
8.705
|
| DEMetro_Z_vs_SMC |
4
|
51.780
|
1.71e-14
|
14.948
|
| HMC_vs_Metro |
0
|
-4.830
|
0.000528
|
-1.394
|
| HMC_vs_Metro |
1
|
-5.710
|
0.000136
|
-1.648
|
| HMC_vs_Metro |
2
|
-4.274
|
0.00131
|
-1.234
|
| HMC_vs_Metro |
3
|
-7.271
|
1.6e-05
|
-2.099
|
| HMC_vs_Metro |
4
|
-4.152
|
0.00161
|
-1.199
|
| Metro_vs_DEMetro_Z |
0
|
3.877
|
0.00257
|
1.119
|
| Metro_vs_DEMetro_Z |
1
|
-30.748
|
5.1e-12
|
-8.876
|
| Metro_vs_DEMetro_Z |
2
|
-14.392
|
1.76e-08
|
-4.155
|
| Metro_vs_DEMetro_Z |
3
|
-18.986
|
9.33e-10
|
-5.481
|
| Metro_vs_DEMetro_Z |
4
|
-21.009
|
3.15e-10
|
-6.065
|
| HMC_vs_SMC |
0
|
3.117
|
0.0098
|
0.900
|
| HMC_vs_SMC |
1
|
4.487
|
0.000921
|
1.295
|
| HMC_vs_SMC |
2
|
6.133
|
7.38e-05
|
1.770
|
| HMC_vs_SMC |
3
|
4.131
|
0.00167
|
1.193
|
| HMC_vs_SMC |
4
|
3.816
|
0.00286
|
1.101
|
| Metro_vs_SMC |
0
|
5.993
|
9.01e-05
|
1.730
|
| Metro_vs_SMC |
1
|
7.352
|
1.44e-05
|
2.122
|
| Metro_vs_SMC |
2
|
4.824
|
0.000532
|
1.393
|
| Metro_vs_SMC |
3
|
8.490
|
3.7e-06
|
2.451
|
| Metro_vs_SMC |
4
|
5.700
|
0.000138
|
1.645
|
| HMC_vs_DEMetro_Z |
0
|
-2.149
|
0.0547
|
-0.620
|
| HMC_vs_DEMetro_Z |
1
|
-45.183
|
7.63e-14
|
-13.043
|
| HMC_vs_DEMetro_Z |
2
|
-28.728
|
1.07e-11
|
-8.293
|
| HMC_vs_DEMetro_Z |
3
|
-29.096
|
9.3e-12
|
-8.399
|
| HMC_vs_DEMetro_Z |
4
|
-35.351
|
1.12e-12
|
-10.205
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.020 |
0.017 |
0.005 |
0.586 |
| HMC |
5 |
0.029 |
0.012 |
0.004 |
4.487 |
| HMC |
10 |
0.023 |
0.014 |
0.005 |
1.794 |
| HMC |
15 |
0.030 |
0.014 |
0.005 |
3.002 |
| HMC |
30 |
0.047 |
0.014 |
0.005 |
7.022 |
| SMC |
2 |
0.012 |
0.017 |
0.005 |
-1.120 |
| SMC |
5 |
0.015 |
0.012 |
0.004 |
0.851 |
| SMC |
10 |
0.013 |
0.014 |
0.005 |
-0.099 |
| SMC |
15 |
0.015 |
0.014 |
0.005 |
0.159 |
| SMC |
30 |
0.017 |
0.014 |
0.005 |
0.652 |
| Metro |
2 |
0.065 |
0.017 |
0.005 |
9.983 |
| Metro |
5 |
0.093 |
0.012 |
0.004 |
20.948 |
| Metro |
10 |
0.117 |
0.014 |
0.005 |
19.642 |
| Metro |
15 |
0.125 |
0.014 |
0.005 |
20.680 |
| Metro |
30 |
0.145 |
0.014 |
0.005 |
28.023 |
| DEMetro_Z |
2 |
0.031 |
0.017 |
0.005 |
2.895 |
| DEMetro_Z |
5 |
0.699 |
0.012 |
0.004 |
176.970 |
| DEMetro_Z |
10 |
0.619 |
0.014 |
0.005 |
114.880 |
| DEMetro_Z |
15 |
0.597 |
0.014 |
0.005 |
109.167 |
| DEMetro_Z |
30 |
0.577 |
0.014 |
0.005 |
120.362 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
R Hat (scatter)
Mode Transitions
One Chain results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
-0.747 |
0.464 |
-0.356 |
| HMC |
5 |
2.880 |
0.0132 |
3.177 |
| HMC |
10 |
3.319 |
0.00478 |
2.489 |
| HMC |
15 |
3.532 |
0.00384 |
3.891 |
| HMC |
30 |
2.893 |
0.0143 |
8.044 |
| SMC |
2 |
-0.601 |
0.554 |
-0.265 |
| SMC |
5 |
0.636 |
0.532 |
0.305 |
| SMC |
10 |
0.335 |
0.74 |
0.147 |
| SMC |
15 |
0.250 |
0.805 |
0.135 |
| SMC |
30 |
0.484 |
0.633 |
0.194 |
| Metro |
2 |
3.644 |
0.0033 |
4.715 |
| Metro |
5 |
4.477 |
0.00091 |
17.139 |
| Metro |
10 |
4.355 |
0.00113 |
24.063 |
| Metro |
15 |
3.710 |
0.0034 |
16.555 |
| Metro |
30 |
4.132 |
0.00165 |
25.481 |
| DEMetro_Z |
2 |
1.491 |
0.154 |
0.905 |
| DEMetro_Z |
5 |
5.557 |
0.000171 |
770.265 |
| DEMetro_Z |
10 |
14.147 |
2.11e-08 |
811.952 |
| DEMetro_Z |
15 |
14.128 |
2.14e-08 |
880.405 |
| DEMetro_Z |
30 |
31.292 |
4.2e-12 |
1077.892 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
-2.067
|
0.0631
|
-0.597
|
| HMC_vs_DEMetro_Z |
1
|
-5.517
|
0.000181
|
-1.593
|
| HMC_vs_DEMetro_Z |
2
|
-14.175
|
2.06e-08
|
-4.092
|
| HMC_vs_DEMetro_Z |
3
|
-14.145
|
2.11e-08
|
-4.083
|
| HMC_vs_DEMetro_Z |
4
|
-30.472
|
5.63e-12
|
-8.796
|
| Metro_vs_SMC |
0
|
4.377
|
0.0011
|
1.264
|
| Metro_vs_SMC |
1
|
4.334
|
0.00119
|
1.251
|
| Metro_vs_SMC |
2
|
4.517
|
0.000877
|
1.304
|
| Metro_vs_SMC |
3
|
3.702
|
0.00349
|
1.069
|
| Metro_vs_SMC |
4
|
4.025
|
0.002
|
1.162
|
| Metro_vs_DEMetro_Z |
0
|
3.330
|
0.00671
|
0.961
|
| Metro_vs_DEMetro_Z |
1
|
-5.478
|
0.000193
|
-1.581
|
| Metro_vs_DEMetro_Z |
2
|
-13.677
|
3e-08
|
-3.948
|
| Metro_vs_DEMetro_Z |
3
|
-14.075
|
2.22e-08
|
-4.063
|
| Metro_vs_DEMetro_Z |
4
|
-32.286
|
3e-12
|
-9.320
|
| HMC_vs_Metro |
0
|
-3.816
|
0.00286
|
-1.102
|
| HMC_vs_Metro |
1
|
-3.525
|
0.00476
|
-1.018
|
| HMC_vs_Metro |
2
|
-3.922
|
0.00238
|
-1.132
|
| HMC_vs_Metro |
3
|
-2.806
|
0.0171
|
-0.810
|
| HMC_vs_Metro |
4
|
-3.361
|
0.00635
|
-0.970
|
| HMC_vs_SMC |
0
|
-0.170
|
0.868
|
-0.049
|
| HMC_vs_SMC |
1
|
2.564
|
0.0263
|
0.740
|
| HMC_vs_SMC |
2
|
3.201
|
0.00844
|
0.924
|
| HMC_vs_SMC |
3
|
3.201
|
0.00845
|
0.924
|
| HMC_vs_SMC |
4
|
2.748
|
0.019
|
0.793
|
| DEMetro_Z_vs_SMC |
0
|
2.003
|
0.0704
|
0.578
|
| DEMetro_Z_vs_SMC |
1
|
5.558
|
0.000171
|
1.604
|
| DEMetro_Z_vs_SMC |
2
|
14.129
|
2.14e-08
|
4.079
|
| DEMetro_Z_vs_SMC |
3
|
14.182
|
2.05e-08
|
4.094
|
| DEMetro_Z_vs_SMC |
4
|
31.270
|
4.25e-12
|
9.027
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.023 |
0.028 |
0.014 |
-0.356 |
| HMC |
5 |
0.039 |
0.015 |
0.007 |
3.177 |
| HMC |
10 |
0.044 |
0.015 |
0.012 |
2.489 |
| HMC |
15 |
0.069 |
0.024 |
0.012 |
3.891 |
| HMC |
30 |
0.110 |
0.018 |
0.011 |
8.044 |
| SMC |
2 |
0.024 |
0.028 |
0.014 |
-0.265 |
| SMC |
5 |
0.017 |
0.015 |
0.007 |
0.305 |
| SMC |
10 |
0.017 |
0.015 |
0.012 |
0.147 |
| SMC |
15 |
0.025 |
0.024 |
0.012 |
0.135 |
| SMC |
30 |
0.020 |
0.018 |
0.011 |
0.194 |
| Metro |
2 |
0.092 |
0.028 |
0.014 |
4.715 |
| Metro |
5 |
0.143 |
0.015 |
0.007 |
17.139 |
| Metro |
10 |
0.292 |
0.015 |
0.012 |
24.063 |
| Metro |
15 |
0.218 |
0.024 |
0.012 |
16.555 |
| Metro |
30 |
0.309 |
0.018 |
0.011 |
25.481 |
| DEMetro_Z |
2 |
0.040 |
0.028 |
0.014 |
0.905 |
| DEMetro_Z |
5 |
5.774 |
0.015 |
0.007 |
770.265 |
| DEMetro_Z |
10 |
9.356 |
0.015 |
0.012 |
811.952 |
| DEMetro_Z |
15 |
10.350 |
0.024 |
0.012 |
880.405 |
| DEMetro_Z |
30 |
12.323 |
0.018 |
0.011 |
1077.892 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
3.107 |
0.00865 |
3.478 |
| HMC |
5 |
2.209 |
0.0452 |
2.032 |
| HMC |
10 |
1.626 |
0.126 |
1.296 |
| HMC |
15 |
3.496 |
0.00423 |
4.158 |
| HMC |
30 |
3.463 |
0.00413 |
3.321 |
| SMC |
2 |
1.382 |
0.184 |
0.803 |
| SMC |
5 |
0.085 |
0.933 |
0.044 |
| SMC |
10 |
-1.064 |
0.303 |
-0.339 |
| SMC |
15 |
0.533 |
0.6 |
0.255 |
| SMC |
30 |
-1.360 |
0.191 |
-0.453 |
| Metro |
2 |
2.826 |
0.0162 |
7.891 |
| Metro |
5 |
4.326 |
0.00106 |
7.535 |
| Metro |
10 |
2.905 |
0.0139 |
6.960 |
| Metro |
15 |
3.390 |
0.00596 |
14.888 |
| Metro |
30 |
6.134 |
6.68e-05 |
16.526 |
| DEMetro_Z |
2 |
3.447 |
0.00405 |
2.997 |
| DEMetro_Z |
5 |
3.661 |
0.00375 |
3797.819 |
| DEMetro_Z |
10 |
6.896 |
2.6e-05 |
1131.907 |
| DEMetro_Z |
15 |
7.473 |
1.24e-05 |
1656.744 |
| DEMetro_Z |
30 |
9.182 |
1.72e-06 |
1001.186 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
3.010
|
0.0119
|
0.869
|
| HMC_vs_SMC |
1
|
1.887
|
0.0858
|
0.545
|
| HMC_vs_SMC |
2
|
1.973
|
0.0741
|
0.570
|
| HMC_vs_SMC |
3
|
3.307
|
0.00699
|
0.955
|
| HMC_vs_SMC |
4
|
3.923
|
0.00238
|
1.132
|
| Metro_vs_DEMetro_Z |
0
|
1.843
|
0.0924
|
0.532
|
| Metro_vs_DEMetro_Z |
1
|
-3.650
|
0.00382
|
-1.054
|
| Metro_vs_DEMetro_Z |
2
|
-6.829
|
2.84e-05
|
-1.971
|
| Metro_vs_DEMetro_Z |
3
|
-7.369
|
1.41e-05
|
-2.127
|
| Metro_vs_DEMetro_Z |
4
|
-9.085
|
1.91e-06
|
-2.623
|
| HMC_vs_Metro |
0
|
-1.368
|
0.198
|
-0.395
|
| HMC_vs_Metro |
1
|
-3.475
|
0.00519
|
-1.003
|
| HMC_vs_Metro |
2
|
-2.224
|
0.048
|
-0.642
|
| HMC_vs_Metro |
3
|
-2.418
|
0.0341
|
-0.698
|
| HMC_vs_Metro |
4
|
-4.700
|
0.000651
|
-1.357
|
| HMC_vs_DEMetro_Z |
0
|
0.386
|
0.707
|
0.111
|
| HMC_vs_DEMetro_Z |
1
|
-3.657
|
0.00377
|
-1.056
|
| HMC_vs_DEMetro_Z |
2
|
-6.869
|
2.7e-05
|
-1.983
|
| HMC_vs_DEMetro_Z |
3
|
-7.457
|
1.27e-05
|
-2.153
|
| HMC_vs_DEMetro_Z |
4
|
-9.168
|
1.75e-06
|
-2.646
|
| Metro_vs_SMC |
0
|
2.506
|
0.0292
|
0.723
|
| Metro_vs_SMC |
1
|
3.814
|
0.00288
|
1.101
|
| Metro_vs_SMC |
2
|
3.108
|
0.00996
|
0.897
|
| Metro_vs_SMC |
3
|
3.205
|
0.00838
|
0.925
|
| Metro_vs_SMC |
4
|
6.430
|
4.87e-05
|
1.856
|
| DEMetro_Z_vs_SMC |
0
|
2.383
|
0.0363
|
0.688
|
| DEMetro_Z_vs_SMC |
1
|
3.661
|
0.00375
|
1.057
|
| DEMetro_Z_vs_SMC |
2
|
6.899
|
2.59e-05
|
1.992
|
| DEMetro_Z_vs_SMC |
3
|
7.482
|
1.23e-05
|
2.160
|
| DEMetro_Z_vs_SMC |
4
|
9.182
|
1.72e-06
|
2.651
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.050 |
0.017 |
0.009 |
3.478 |
| HMC |
5 |
0.048 |
0.025 |
0.011 |
2.032 |
| HMC |
10 |
0.056 |
0.032 |
0.019 |
1.296 |
| HMC |
15 |
0.071 |
0.024 |
0.011 |
4.158 |
| HMC |
30 |
0.096 |
0.032 |
0.019 |
3.321 |
| SMC |
2 |
0.025 |
0.017 |
0.009 |
0.803 |
| SMC |
5 |
0.026 |
0.025 |
0.011 |
0.044 |
| SMC |
10 |
0.025 |
0.032 |
0.019 |
-0.339 |
| SMC |
15 |
0.027 |
0.024 |
0.011 |
0.255 |
| SMC |
30 |
0.024 |
0.032 |
0.019 |
-0.453 |
| Metro |
2 |
0.092 |
0.017 |
0.009 |
7.891 |
| Metro |
5 |
0.110 |
0.025 |
0.011 |
7.535 |
| Metro |
10 |
0.162 |
0.032 |
0.019 |
6.960 |
| Metro |
15 |
0.194 |
0.024 |
0.011 |
14.888 |
| Metro |
30 |
0.347 |
0.032 |
0.019 |
16.526 |
| DEMetro_Z |
2 |
0.046 |
0.017 |
0.009 |
2.997 |
| DEMetro_Z |
5 |
42.769 |
0.025 |
0.011 |
3797.819 |
| DEMetro_Z |
10 |
21.217 |
0.032 |
0.019 |
1131.907 |
| DEMetro_Z |
15 |
18.933 |
0.024 |
0.011 |
1656.744 |
| DEMetro_Z |
30 |
19.067 |
0.032 |
0.019 |
1001.186 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
0.334 |
0.742 |
0.179 |
| HMC |
5 |
3.670 |
0.00292 |
3.930 |
| HMC |
10 |
4.969 |
0.000191 |
3.891 |
| HMC |
15 |
4.864 |
0.000369 |
6.103 |
| HMC |
30 |
3.050 |
0.0109 |
12.884 |
| SMC |
2 |
-0.552 |
0.587 |
-0.259 |
| SMC |
5 |
0.636 |
0.533 |
0.357 |
| SMC |
10 |
-0.215 |
0.832 |
-0.097 |
| SMC |
15 |
0.877 |
0.393 |
0.536 |
| SMC |
30 |
1.028 |
0.315 |
0.454 |
| Metro |
2 |
4.643 |
0.000607 |
7.675 |
| Metro |
5 |
5.040 |
0.000369 |
22.687 |
| Metro |
10 |
4.742 |
0.000603 |
35.314 |
| Metro |
15 |
5.203 |
0.000288 |
29.016 |
| Metro |
30 |
5.704 |
0.000136 |
47.958 |
| DEMetro_Z |
2 |
2.090 |
0.054 |
1.496 |
| DEMetro_Z |
5 |
5.376 |
0.000225 |
1044.981 |
| DEMetro_Z |
10 |
13.246 |
4.19e-08 |
1223.253 |
| DEMetro_Z |
15 |
15.029 |
1.12e-08 |
1353.310 |
| DEMetro_Z |
30 |
25.785 |
3.45e-11 |
1760.089 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
4.289
|
0.00128
|
1.238
|
| Metro_vs_DEMetro_Z |
1
|
-5.299
|
0.000253
|
-1.530
|
| Metro_vs_DEMetro_Z |
2
|
-12.843
|
5.77e-08
|
-3.707
|
| Metro_vs_DEMetro_Z |
3
|
-14.934
|
1.19e-08
|
-4.311
|
| Metro_vs_DEMetro_Z |
4
|
-26.054
|
3.08e-11
|
-7.521
|
| DEMetro_Z_vs_SMC |
0
|
2.913
|
0.0141
|
0.841
|
| DEMetro_Z_vs_SMC |
1
|
5.376
|
0.000225
|
1.552
|
| DEMetro_Z_vs_SMC |
2
|
13.231
|
4.24e-08
|
3.819
|
| DEMetro_Z_vs_SMC |
3
|
15.072
|
1.08e-08
|
4.351
|
| DEMetro_Z_vs_SMC |
4
|
25.760
|
3.49e-11
|
7.436
|
| HMC_vs_DEMetro_Z |
0
|
-2.059
|
0.064
|
-0.594
|
| HMC_vs_DEMetro_Z |
1
|
-5.342
|
0.000237
|
-1.542
|
| HMC_vs_DEMetro_Z |
2
|
-13.211
|
4.31e-08
|
-3.814
|
| HMC_vs_DEMetro_Z |
3
|
-15.017
|
1.13e-08
|
-4.335
|
| HMC_vs_DEMetro_Z |
4
|
-25.469
|
3.94e-11
|
-7.352
|
| HMC_vs_Metro |
0
|
-4.939
|
0.000443
|
-1.426
|
| HMC_vs_Metro |
1
|
-3.934
|
0.00234
|
-1.136
|
| HMC_vs_Metro |
2
|
-4.164
|
0.00158
|
-1.202
|
| HMC_vs_Metro |
3
|
-3.839
|
0.00275
|
-1.108
|
| HMC_vs_Metro |
4
|
-4.695
|
0.000655
|
-1.355
|
| HMC_vs_SMC |
0
|
1.172
|
0.266
|
0.338
|
| HMC_vs_SMC |
1
|
3.304
|
0.00703
|
0.954
|
| HMC_vs_SMC |
2
|
5.146
|
0.00032
|
1.486
|
| HMC_vs_SMC |
3
|
3.893
|
0.00251
|
1.124
|
| HMC_vs_SMC |
4
|
2.876
|
0.0151
|
0.830
|
| Metro_vs_SMC |
0
|
5.423
|
0.000209
|
1.565
|
| Metro_vs_SMC |
1
|
4.752
|
0.000598
|
1.372
|
| Metro_vs_SMC |
2
|
4.908
|
0.000466
|
1.417
|
| Metro_vs_SMC |
3
|
5.135
|
0.000326
|
1.482
|
| Metro_vs_SMC |
4
|
5.614
|
0.000157
|
1.621
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.035 |
0.033 |
0.009 |
0.179 |
| HMC |
5 |
0.042 |
0.022 |
0.005 |
3.930 |
| HMC |
10 |
0.050 |
0.023 |
0.007 |
3.891 |
| HMC |
15 |
0.065 |
0.025 |
0.007 |
6.103 |
| HMC |
30 |
0.098 |
0.024 |
0.006 |
12.884 |
| SMC |
2 |
0.031 |
0.033 |
0.009 |
-0.259 |
| SMC |
5 |
0.024 |
0.022 |
0.005 |
0.357 |
| SMC |
10 |
0.023 |
0.023 |
0.007 |
-0.097 |
| SMC |
15 |
0.029 |
0.025 |
0.007 |
0.536 |
| SMC |
30 |
0.026 |
0.024 |
0.006 |
0.454 |
| Metro |
2 |
0.101 |
0.033 |
0.009 |
7.675 |
| Metro |
5 |
0.135 |
0.022 |
0.005 |
22.687 |
| Metro |
10 |
0.261 |
0.023 |
0.007 |
35.314 |
| Metro |
15 |
0.216 |
0.025 |
0.007 |
29.016 |
| Metro |
30 |
0.301 |
0.024 |
0.006 |
47.958 |
| DEMetro_Z |
2 |
0.046 |
0.033 |
0.009 |
1.496 |
| DEMetro_Z |
5 |
5.212 |
0.022 |
0.005 |
1044.981 |
| DEMetro_Z |
10 |
8.274 |
0.023 |
0.007 |
1223.253 |
| DEMetro_Z |
15 |
8.907 |
0.025 |
0.007 |
1353.310 |
| DEMetro_Z |
30 |
10.215 |
0.024 |
0.006 |
1760.089 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
0.312 |
0.759 |
0.218 |
| HMC |
5 |
3.704 |
0.00261 |
3.595 |
| HMC |
10 |
4.594 |
0.000312 |
3.083 |
| HMC |
15 |
5.355 |
0.000102 |
4.426 |
| HMC |
30 |
2.819 |
0.0164 |
8.435 |
| SMC |
2 |
-0.418 |
0.68 |
-0.172 |
| SMC |
5 |
0.562 |
0.58 |
0.271 |
| SMC |
10 |
-1.210 |
0.239 |
-0.467 |
| SMC |
15 |
0.536 |
0.598 |
0.284 |
| SMC |
30 |
0.792 |
0.437 |
0.345 |
| Metro |
2 |
5.841 |
8.29e-05 |
8.613 |
| Metro |
5 |
5.550 |
0.000162 |
16.719 |
| Metro |
10 |
5.560 |
0.000166 |
28.051 |
| Metro |
15 |
6.024 |
8.3e-05 |
25.286 |
| Metro |
30 |
7.076 |
2e-05 |
40.571 |
| DEMetro_Z |
2 |
1.615 |
0.127 |
1.129 |
| DEMetro_Z |
5 |
11.435 |
1.89e-07 |
150.159 |
| DEMetro_Z |
10 |
35.098 |
1.04e-12 |
173.085 |
| DEMetro_Z |
15 |
56.083 |
4.43e-15 |
169.724 |
| DEMetro_Z |
30 |
43.859 |
8.81e-14 |
203.778 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
2.503
|
0.0293
|
0.723
|
| DEMetro_Z_vs_SMC |
1
|
11.302
|
2.15e-07
|
3.262
|
| DEMetro_Z_vs_SMC |
2
|
35.004
|
1.24e-12
|
10.105
|
| DEMetro_Z_vs_SMC |
3
|
56.154
|
7.05e-15
|
16.210
|
| DEMetro_Z_vs_SMC |
4
|
45.179
|
7.64e-14
|
13.042
|
| HMC_vs_Metro |
0
|
-6.099
|
7.74e-05
|
-1.761
|
| HMC_vs_Metro |
1
|
-3.964
|
0.00222
|
-1.144
|
| HMC_vs_Metro |
2
|
-4.816
|
0.000539
|
-1.390
|
| HMC_vs_Metro |
3
|
-4.693
|
0.000658
|
-1.355
|
| HMC_vs_Metro |
4
|
-6.364
|
5.34e-05
|
-1.837
|
| Metro_vs_DEMetro_Z |
0
|
6.747
|
3.17e-05
|
1.948
|
| Metro_vs_DEMetro_Z |
1
|
-11.172
|
2.42e-07
|
-3.225
|
| Metro_vs_DEMetro_Z |
2
|
-18.585
|
1.17e-09
|
-5.365
|
| Metro_vs_DEMetro_Z |
3
|
-29.836
|
7.08e-12
|
-8.613
|
| Metro_vs_DEMetro_Z |
4
|
-18.991
|
9.31e-10
|
-5.482
|
| HMC_vs_SMC |
0
|
0.820
|
0.43
|
0.237
|
| HMC_vs_SMC |
1
|
4.039
|
0.00195
|
1.166
|
| HMC_vs_SMC |
2
|
5.809
|
0.000118
|
1.677
|
| HMC_vs_SMC |
3
|
4.362
|
0.00113
|
1.259
|
| HMC_vs_SMC |
4
|
2.650
|
0.0226
|
0.765
|
| Metro_vs_SMC |
0
|
6.698
|
3.38e-05
|
1.934
|
| Metro_vs_SMC |
1
|
5.090
|
0.00035
|
1.469
|
| Metro_vs_SMC |
2
|
5.794
|
0.00012
|
1.673
|
| Metro_vs_SMC |
3
|
5.976
|
9.24e-05
|
1.725
|
| Metro_vs_SMC |
4
|
6.976
|
2.34e-05
|
2.014
|
| HMC_vs_DEMetro_Z |
0
|
-1.471
|
0.169
|
-0.425
|
| HMC_vs_DEMetro_Z |
1
|
-11.154
|
2.46e-07
|
-3.220
|
| HMC_vs_DEMetro_Z |
2
|
-33.810
|
1.81e-12
|
-9.760
|
| HMC_vs_DEMetro_Z |
3
|
-50.272
|
2.37e-14
|
-14.512
|
| HMC_vs_DEMetro_Z |
4
|
-29.980
|
6.71e-12
|
-8.655
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.018 |
0.017 |
0.005 |
0.218 |
| HMC |
5 |
0.026 |
0.012 |
0.004 |
3.595 |
| HMC |
10 |
0.030 |
0.014 |
0.005 |
3.083 |
| HMC |
15 |
0.038 |
0.014 |
0.005 |
4.426 |
| HMC |
30 |
0.053 |
0.014 |
0.005 |
8.435 |
| SMC |
2 |
0.017 |
0.017 |
0.005 |
-0.172 |
| SMC |
5 |
0.013 |
0.012 |
0.004 |
0.271 |
| SMC |
10 |
0.011 |
0.014 |
0.005 |
-0.467 |
| SMC |
15 |
0.016 |
0.014 |
0.005 |
0.284 |
| SMC |
30 |
0.016 |
0.014 |
0.005 |
0.345 |
| Metro |
2 |
0.059 |
0.017 |
0.005 |
8.613 |
| Metro |
5 |
0.077 |
0.012 |
0.004 |
16.719 |
| Metro |
10 |
0.162 |
0.014 |
0.005 |
28.051 |
| Metro |
15 |
0.149 |
0.014 |
0.005 |
25.286 |
| Metro |
30 |
0.204 |
0.014 |
0.005 |
40.571 |
| DEMetro_Z |
2 |
0.023 |
0.017 |
0.005 |
1.129 |
| DEMetro_Z |
5 |
0.595 |
0.012 |
0.004 |
150.159 |
| DEMetro_Z |
10 |
0.925 |
0.014 |
0.005 |
173.085 |
| DEMetro_Z |
15 |
0.921 |
0.014 |
0.005 |
169.724 |
| DEMetro_Z |
30 |
0.967 |
0.014 |
0.005 |
203.778 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
Mode Transitions
KDE + Init Plots
Forest & Ridge Plots
Pooled
Chain
Pairwise Scatter Plots
Pooled
Chain
Vary_Dimension_with_heavy_Tails
(MvStudentT,
dimension,
12 runs)
Pooled Chains results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
-1.109 |
0.28 |
-0.409 |
| HMC |
5 |
1.132 |
0.277 |
0.961 |
| HMC |
10 |
1.520 |
0.156 |
3.018 |
| HMC |
15 |
0.379 |
0.709 |
0.209 |
| HMC |
30 |
1.118 |
0.287 |
33.826 |
| SMC |
2 |
-0.602 |
0.555 |
-0.196 |
| SMC |
5 |
4.519 |
0.000687 |
5.952 |
| SMC |
10 |
6.429 |
3.96e-05 |
12.364 |
| SMC |
15 |
9.854 |
1.27e-08 |
5.627 |
| SMC |
30 |
15.641 |
1.07e-09 |
16.561 |
| Metro |
2 |
0.661 |
0.516 |
0.282 |
| Metro |
5 |
4.958 |
0.000104 |
2.809 |
| Metro |
10 |
4.151 |
0.00133 |
5.565 |
| Metro |
15 |
2.852 |
0.0112 |
1.757 |
| Metro |
30 |
3.777 |
0.00302 |
17.125 |
| DEMetro_Z |
2 |
1.784 |
0.0883 |
0.751 |
| DEMetro_Z |
5 |
5.149 |
0.000319 |
141.883 |
| DEMetro_Z |
10 |
5.190 |
0.000299 |
150.517 |
| DEMetro_Z |
15 |
8.244 |
4.8e-06 |
59.111 |
| DEMetro_Z |
30 |
11.501 |
1.8e-07 |
767.340 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
-3.285
|
0.00727
|
-0.948
|
| HMC_vs_DEMetro_Z |
1
|
-5.094
|
0.000347
|
-1.470
|
| HMC_vs_DEMetro_Z |
2
|
-5.078
|
0.000356
|
-1.466
|
| HMC_vs_DEMetro_Z |
3
|
-8.195
|
5.19e-06
|
-2.366
|
| HMC_vs_DEMetro_Z |
4
|
-10.464
|
4.69e-07
|
-3.021
|
| Metro_vs_SMC |
0
|
1.739
|
0.11
|
0.502
|
| Metro_vs_SMC |
1
|
-2.372
|
0.0371
|
-0.685
|
| Metro_vs_SMC |
2
|
-2.577
|
0.0257
|
-0.744
|
| Metro_vs_SMC |
3
|
-5.668
|
0.000145
|
-1.636
|
| Metro_vs_SMC |
4
|
0.130
|
0.899
|
0.037
|
| Metro_vs_DEMetro_Z |
0
|
-1.066
|
0.309
|
-0.308
|
| Metro_vs_DEMetro_Z |
1
|
-5.001
|
0.000402
|
-1.444
|
| Metro_vs_DEMetro_Z |
2
|
-4.961
|
0.000428
|
-1.432
|
| Metro_vs_DEMetro_Z |
3
|
-8.115
|
5.7e-06
|
-2.343
|
| Metro_vs_DEMetro_Z |
4
|
-11.010
|
2.8e-07
|
-3.178
|
| HMC_vs_Metro |
0
|
-2.116
|
0.058
|
-0.611
|
| HMC_vs_Metro |
1
|
-2.020
|
0.0684
|
-0.583
|
| HMC_vs_Metro |
2
|
-1.825
|
0.0953
|
-0.527
|
| HMC_vs_Metro |
3
|
-2.213
|
0.0489
|
-0.639
|
| HMC_vs_Metro |
4
|
0.528
|
0.608
|
0.152
|
| HMC_vs_SMC |
0
|
-0.920
|
0.377
|
-0.266
|
| HMC_vs_SMC |
1
|
-3.077
|
0.0105
|
-0.888
|
| HMC_vs_SMC |
2
|
-3.577
|
0.00434
|
-1.033
|
| HMC_vs_SMC |
3
|
-8.477
|
3.75e-06
|
-2.447
|
| HMC_vs_SMC |
4
|
0.570
|
0.58
|
0.165
|
| DEMetro_Z_vs_SMC |
0
|
3.024
|
0.0116
|
0.873
|
| DEMetro_Z_vs_SMC |
1
|
4.913
|
0.000462
|
1.418
|
| DEMetro_Z_vs_SMC |
2
|
4.638
|
0.000719
|
1.339
|
| DEMetro_Z_vs_SMC |
3
|
7.287
|
1.57e-05
|
2.104
|
| DEMetro_Z_vs_SMC |
4
|
11.230
|
2.29e-07
|
3.242
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.056 |
0.072 |
0.040 |
-0.409 |
| HMC |
5 |
0.076 |
0.053 |
0.023 |
0.961 |
| HMC |
10 |
0.109 |
0.065 |
0.015 |
3.018 |
| HMC |
15 |
0.080 |
0.073 |
0.032 |
0.209 |
| HMC |
30 |
0.342 |
0.066 |
0.008 |
33.826 |
| SMC |
2 |
0.064 |
0.072 |
0.040 |
-0.196 |
| SMC |
5 |
0.191 |
0.053 |
0.023 |
5.952 |
| SMC |
10 |
0.247 |
0.065 |
0.015 |
12.364 |
| SMC |
15 |
0.252 |
0.073 |
0.032 |
5.627 |
| SMC |
30 |
0.201 |
0.066 |
0.008 |
16.561 |
| Metro |
2 |
0.083 |
0.072 |
0.040 |
0.282 |
| Metro |
5 |
0.118 |
0.053 |
0.023 |
2.809 |
| Metro |
10 |
0.147 |
0.065 |
0.015 |
5.565 |
| Metro |
15 |
0.129 |
0.073 |
0.032 |
1.757 |
| Metro |
30 |
0.206 |
0.066 |
0.008 |
17.125 |
| DEMetro_Z |
2 |
0.102 |
0.072 |
0.040 |
0.751 |
| DEMetro_Z |
5 |
3.329 |
0.053 |
0.023 |
141.883 |
| DEMetro_Z |
10 |
2.282 |
0.065 |
0.015 |
150.517 |
| DEMetro_Z |
15 |
1.957 |
0.073 |
0.032 |
59.111 |
| DEMetro_Z |
30 |
6.342 |
0.066 |
0.008 |
767.340 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
-0.030 |
0.976 |
-0.012 |
| HMC |
5 |
-0.360 |
0.723 |
-0.138 |
| HMC |
10 |
1.626 |
0.132 |
4.841 |
| HMC |
15 |
-0.894 |
0.387 |
-0.273 |
| HMC |
30 |
1.075 |
0.305 |
9.498 |
| SMC |
2 |
-0.071 |
0.944 |
-0.027 |
| SMC |
5 |
3.343 |
0.00408 |
2.160 |
| SMC |
10 |
17.480 |
3.59e-11 |
13.379 |
| SMC |
15 |
5.240 |
0.000178 |
1.566 |
| SMC |
30 |
32.543 |
1.13e-14 |
26.465 |
| Metro |
2 |
-0.130 |
0.898 |
-0.049 |
| Metro |
5 |
-1.486 |
0.159 |
-0.460 |
| Metro |
10 |
2.062 |
0.0584 |
1.733 |
| Metro |
15 |
-1.257 |
0.233 |
-0.371 |
| Metro |
30 |
1.036 |
0.322 |
4.254 |
| DEMetro_Z |
2 |
0.035 |
0.973 |
0.014 |
| DEMetro_Z |
5 |
3.512 |
0.00487 |
141.501 |
| DEMetro_Z |
10 |
3.759 |
0.00316 |
60.947 |
| DEMetro_Z |
15 |
3.578 |
0.00305 |
2.993 |
| DEMetro_Z |
30 |
8.425 |
3.96e-06 |
151.735 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
0.514
|
0.618
|
0.148
|
| HMC_vs_SMC |
1
|
-3.434
|
0.00558
|
-0.991
|
| HMC_vs_SMC |
2
|
-2.415
|
0.0343
|
-0.697
|
| HMC_vs_SMC |
3
|
-15.661
|
7.23e-09
|
-4.521
|
| HMC_vs_SMC |
4
|
-1.924
|
0.0806
|
-0.555
|
| Metro_vs_DEMetro_Z |
0
|
-1.879
|
0.087
|
-0.542
|
| Metro_vs_DEMetro_Z |
1
|
-3.521
|
0.00479
|
-1.016
|
| Metro_vs_DEMetro_Z |
2
|
-3.627
|
0.00398
|
-1.047
|
| Metro_vs_DEMetro_Z |
3
|
-4.255
|
0.00135
|
-1.228
|
| Metro_vs_DEMetro_Z |
4
|
-7.502
|
1.2e-05
|
-2.166
|
| HMC_vs_Metro |
0
|
0.822
|
0.428
|
0.237
|
| HMC_vs_Metro |
1
|
1.180
|
0.263
|
0.341
|
| HMC_vs_Metro |
2
|
1.003
|
0.338
|
0.289
|
| HMC_vs_Metro |
3
|
1.014
|
0.333
|
0.293
|
| HMC_vs_Metro |
4
|
0.517
|
0.615
|
0.149
|
| HMC_vs_DEMetro_Z |
0
|
-0.487
|
0.636
|
-0.141
|
| HMC_vs_DEMetro_Z |
1
|
-3.523
|
0.00477
|
-1.017
|
| HMC_vs_DEMetro_Z |
2
|
-4.083
|
0.00181
|
-1.179
|
| HMC_vs_DEMetro_Z |
3
|
-4.393
|
0.00108
|
-1.268
|
| HMC_vs_DEMetro_Z |
4
|
-8.159
|
5.42e-06
|
-2.355
|
| Metro_vs_SMC |
0
|
-0.378
|
0.712
|
-0.109
|
| Metro_vs_SMC |
1
|
-4.847
|
0.000513
|
-1.399
|
| Metro_vs_SMC |
2
|
-11.526
|
1.76e-07
|
-3.327
|
| Metro_vs_SMC |
3
|
-17.453
|
2.29e-09
|
-5.038
|
| Metro_vs_SMC |
4
|
-5.169
|
0.000309
|
-1.492
|
| DEMetro_Z_vs_SMC |
0
|
0.599
|
0.562
|
0.173
|
| DEMetro_Z_vs_SMC |
1
|
3.460
|
0.00533
|
0.999
|
| DEMetro_Z_vs_SMC |
2
|
2.862
|
0.0155
|
0.826
|
| DEMetro_Z_vs_SMC |
3
|
1.823
|
0.0956
|
0.526
|
| DEMetro_Z_vs_SMC |
4
|
7.037
|
2.16e-05
|
2.031
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
8.602 |
8.779 |
15.112 |
-0.012 |
| HMC |
5 |
4.400 |
5.105 |
5.103 |
-0.138 |
| HMC |
10 |
19.832 |
3.930 |
3.285 |
4.841 |
| HMC |
15 |
9.277 |
17.964 |
31.848 |
-0.273 |
| HMC |
30 |
39.346 |
4.774 |
3.640 |
9.498 |
| SMC |
2 |
8.370 |
8.779 |
15.112 |
-0.027 |
| SMC |
5 |
16.128 |
5.105 |
5.103 |
2.160 |
| SMC |
10 |
47.875 |
3.930 |
3.285 |
13.379 |
| SMC |
15 |
67.838 |
17.964 |
31.848 |
1.566 |
| SMC |
30 |
101.103 |
4.774 |
3.640 |
26.465 |
| Metro |
2 |
8.038 |
8.779 |
15.112 |
-0.049 |
| Metro |
5 |
2.760 |
5.105 |
5.103 |
-0.460 |
| Metro |
10 |
9.620 |
3.930 |
3.285 |
1.733 |
| Metro |
15 |
6.141 |
17.964 |
31.848 |
-0.371 |
| Metro |
30 |
20.259 |
4.774 |
3.640 |
4.254 |
| DEMetro_Z |
2 |
8.987 |
8.779 |
15.112 |
0.014 |
| DEMetro_Z |
5 |
727.202 |
5.105 |
5.103 |
141.501 |
| DEMetro_Z |
10 |
204.123 |
3.930 |
3.285 |
60.947 |
| DEMetro_Z |
15 |
113.275 |
17.964 |
31.848 |
2.993 |
| DEMetro_Z |
30 |
557.075 |
4.774 |
3.640 |
151.735 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
1.815 |
0.0847 |
0.902 |
| HMC |
5 |
3.277 |
0.00681 |
5.310 |
| HMC |
10 |
3.058 |
0.0108 |
14.158 |
| HMC |
15 |
3.023 |
0.0105 |
3.882 |
| HMC |
30 |
1.566 |
0.146 |
73.364 |
| SMC |
2 |
0.780 |
0.444 |
0.328 |
| SMC |
5 |
10.543 |
4.24e-07 |
79.507 |
| SMC |
10 |
28.772 |
1.02e-11 |
291.834 |
| SMC |
15 |
41.413 |
1.32e-13 |
127.591 |
| SMC |
30 |
72.168 |
4.13e-16 |
546.646 |
| Metro |
2 |
3.066 |
0.00636 |
1.611 |
| Metro |
5 |
5.330 |
0.000142 |
5.485 |
| Metro |
10 |
4.306 |
0.00121 |
16.898 |
| Metro |
15 |
3.057 |
0.00971 |
3.723 |
| Metro |
30 |
2.256 |
0.0454 |
45.915 |
| DEMetro_Z |
2 |
5.516 |
4.5e-05 |
3.554 |
| DEMetro_Z |
5 |
5.673 |
0.000144 |
658.767 |
| DEMetro_Z |
10 |
8.842 |
2.49e-06 |
583.946 |
| DEMetro_Z |
15 |
10.080 |
6.79e-07 |
151.545 |
| DEMetro_Z |
30 |
16.754 |
3.54e-09 |
1334.969 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
-3.772
|
0.00309
|
-1.089
|
| Metro_vs_DEMetro_Z |
1
|
-5.614
|
0.000157
|
-1.621
|
| Metro_vs_DEMetro_Z |
2
|
-8.401
|
4.09e-06
|
-2.425
|
| Metro_vs_DEMetro_Z |
3
|
-10.046
|
7.06e-07
|
-2.900
|
| Metro_vs_DEMetro_Z |
4
|
-14.982
|
1.15e-08
|
-4.325
|
| DEMetro_Z_vs_SMC |
0
|
5.689
|
0.00014
|
1.642
|
| DEMetro_Z_vs_SMC |
1
|
4.990
|
0.000409
|
1.440
|
| DEMetro_Z_vs_SMC |
2
|
4.238
|
0.00139
|
1.223
|
| DEMetro_Z_vs_SMC |
3
|
1.533
|
0.154
|
0.442
|
| DEMetro_Z_vs_SMC |
4
|
10.100
|
6.69e-07
|
2.916
|
| HMC_vs_DEMetro_Z |
0
|
-3.761
|
0.00315
|
-1.086
|
| HMC_vs_DEMetro_Z |
1
|
-5.618
|
0.000156
|
-1.622
|
| HMC_vs_DEMetro_Z |
2
|
-8.940
|
2.24e-06
|
-2.581
|
| HMC_vs_DEMetro_Z |
3
|
-10.279
|
5.61e-07
|
-2.967
|
| HMC_vs_DEMetro_Z |
4
|
-17.946
|
1.7e-09
|
-5.181
|
| HMC_vs_Metro |
0
|
-1.459
|
0.173
|
-0.421
|
| HMC_vs_Metro |
1
|
-0.116
|
0.91
|
-0.033
|
| HMC_vs_Metro |
2
|
-0.505
|
0.623
|
-0.146
|
| HMC_vs_Metro |
3
|
0.086
|
0.933
|
0.025
|
| HMC_vs_Metro |
4
|
0.517
|
0.616
|
0.149
|
| HMC_vs_SMC |
0
|
2.130
|
0.0566
|
0.615
|
| HMC_vs_SMC |
1
|
-8.888
|
2.37e-06
|
-2.566
|
| HMC_vs_SMC |
2
|
-20.188
|
4.83e-10
|
-5.828
|
| HMC_vs_SMC |
3
|
-41.086
|
2.16e-13
|
-11.861
|
| HMC_vs_SMC |
4
|
-10.062
|
6.95e-07
|
-2.905
|
| Metro_vs_SMC |
0
|
3.097
|
0.0102
|
0.894
|
| Metro_vs_SMC |
1
|
-9.698
|
1e-06
|
-2.799
|
| Metro_vs_SMC |
2
|
-24.813
|
5.23e-11
|
-7.163
|
| Metro_vs_SMC |
3
|
-33.336
|
2.11e-12
|
-9.623
|
| Metro_vs_SMC |
4
|
-22.204
|
1.74e-10
|
-6.410
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.156 |
0.122 |
0.038 |
0.902 |
| HMC |
5 |
0.194 |
0.113 |
0.015 |
5.310 |
| HMC |
10 |
0.296 |
0.110 |
0.013 |
14.158 |
| HMC |
15 |
0.283 |
0.131 |
0.039 |
3.882 |
| HMC |
30 |
1.006 |
0.111 |
0.012 |
73.364 |
| SMC |
2 |
0.134 |
0.122 |
0.038 |
0.328 |
| SMC |
5 |
1.330 |
0.113 |
0.015 |
79.507 |
| SMC |
10 |
3.955 |
0.110 |
0.013 |
291.834 |
| SMC |
15 |
5.120 |
0.131 |
0.039 |
127.591 |
| SMC |
30 |
6.784 |
0.111 |
0.012 |
546.646 |
| Metro |
2 |
0.183 |
0.122 |
0.038 |
1.611 |
| Metro |
5 |
0.197 |
0.113 |
0.015 |
5.485 |
| Metro |
10 |
0.332 |
0.110 |
0.013 |
16.898 |
| Metro |
15 |
0.277 |
0.131 |
0.039 |
3.723 |
| Metro |
30 |
0.671 |
0.111 |
0.012 |
45.915 |
| DEMetro_Z |
2 |
0.256 |
0.122 |
0.038 |
3.554 |
| DEMetro_Z |
5 |
10.202 |
0.113 |
0.015 |
658.767 |
| DEMetro_Z |
10 |
7.804 |
0.110 |
0.013 |
583.946 |
| DEMetro_Z |
15 |
6.056 |
0.131 |
0.039 |
151.545 |
| DEMetro_Z |
30 |
16.409 |
0.111 |
0.012 |
1334.969 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
1.934 |
0.0662 |
0.831 |
| HMC |
5 |
2.612 |
0.024 |
10.558 |
| HMC |
10 |
2.434 |
0.0331 |
17.961 |
| HMC |
15 |
3.034 |
0.0113 |
15.931 |
| HMC |
30 |
3.024 |
0.0116 |
82.178 |
| SMC |
2 |
1.648 |
0.118 |
0.985 |
| SMC |
5 |
20.420 |
3.82e-10 |
96.840 |
| SMC |
10 |
80.298 |
6.41e-17 |
205.177 |
| SMC |
15 |
93.490 |
7.66e-18 |
195.454 |
| SMC |
30 |
87.610 |
3.91e-17 |
357.325 |
| Metro |
2 |
5.302 |
6.45e-05 |
3.326 |
| Metro |
5 |
8.520 |
1.79e-06 |
10.967 |
| Metro |
10 |
5.988 |
8.63e-05 |
21.986 |
| Metro |
15 |
6.141 |
6.8e-05 |
19.603 |
| Metro |
30 |
6.462 |
4.64e-05 |
73.960 |
| DEMetro_Z |
2 |
5.822 |
6.24e-05 |
6.014 |
| DEMetro_Z |
5 |
14.209 |
1.99e-08 |
186.419 |
| DEMetro_Z |
10 |
30.408 |
5.47e-12 |
243.808 |
| DEMetro_Z |
15 |
31.611 |
3.51e-12 |
215.608 |
| DEMetro_Z |
30 |
49.074 |
2.93e-14 |
436.952 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
4.875
|
0.000491
|
1.407
|
| DEMetro_Z_vs_SMC |
1
|
6.751
|
3.15e-05
|
1.949
|
| DEMetro_Z_vs_SMC |
2
|
4.869
|
0.000495
|
1.406
|
| DEMetro_Z_vs_SMC |
3
|
2.879
|
0.015
|
0.831
|
| DEMetro_Z_vs_SMC |
4
|
8.516
|
3.59e-06
|
2.458
|
| HMC_vs_Metro |
0
|
-3.647
|
0.00384
|
-1.053
|
| HMC_vs_Metro |
1
|
-0.094
|
0.927
|
-0.027
|
| HMC_vs_Metro |
2
|
-0.658
|
0.524
|
-0.190
|
| HMC_vs_Metro |
3
|
-0.584
|
0.571
|
-0.168
|
| HMC_vs_Metro |
4
|
0.282
|
0.783
|
0.081
|
| Metro_vs_DEMetro_Z |
0
|
-2.031
|
0.0671
|
-0.586
|
| Metro_vs_DEMetro_Z |
1
|
-13.447
|
3.58e-08
|
-3.882
|
| Metro_vs_DEMetro_Z |
2
|
-20.516
|
4.07e-10
|
-5.923
|
| Metro_vs_DEMetro_Z |
3
|
-29.753
|
7.3e-12
|
-8.589
|
| Metro_vs_DEMetro_Z |
4
|
-28.660
|
1.1e-11
|
-8.273
|
| HMC_vs_SMC |
0
|
-0.321
|
0.754
|
-0.093
|
| HMC_vs_SMC |
1
|
-12.153
|
1.02e-07
|
-3.508
|
| HMC_vs_SMC |
2
|
-24.642
|
5.64e-11
|
-7.114
|
| HMC_vs_SMC |
3
|
-33.678
|
1.89e-12
|
-9.722
|
| HMC_vs_SMC |
4
|
-10.005
|
7.36e-07
|
-2.888
|
| Metro_vs_SMC |
0
|
3.420
|
0.00572
|
0.987
|
| Metro_vs_SMC |
1
|
-17.348
|
2.44e-09
|
-5.008
|
| Metro_vs_SMC |
2
|
-39.360
|
3.45e-13
|
-11.362
|
| Metro_vs_SMC |
3
|
-38.403
|
4.52e-13
|
-11.086
|
| Metro_vs_SMC |
4
|
-22.978
|
1.2e-10
|
-6.633
|
| HMC_vs_DEMetro_Z |
0
|
-4.978
|
0.000416
|
-1.437
|
| HMC_vs_DEMetro_Z |
1
|
-14.162
|
2.08e-08
|
-4.088
|
| HMC_vs_DEMetro_Z |
2
|
-18.766
|
1.06e-09
|
-5.417
|
| HMC_vs_DEMetro_Z |
3
|
-24.016
|
7.45e-11
|
-6.933
|
| HMC_vs_DEMetro_Z |
4
|
-14.089
|
2.2e-08
|
-4.067
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.018 |
0.014 |
0.004 |
0.831 |
| HMC |
5 |
0.038 |
0.014 |
0.002 |
10.558 |
| HMC |
10 |
0.048 |
0.015 |
0.002 |
17.961 |
| HMC |
15 |
0.046 |
0.015 |
0.002 |
15.931 |
| HMC |
30 |
0.103 |
0.015 |
0.001 |
82.178 |
| SMC |
2 |
0.019 |
0.014 |
0.004 |
0.985 |
| SMC |
5 |
0.231 |
0.014 |
0.002 |
96.840 |
| SMC |
10 |
0.399 |
0.015 |
0.002 |
205.177 |
| SMC |
15 |
0.399 |
0.015 |
0.002 |
195.454 |
| SMC |
30 |
0.396 |
0.015 |
0.001 |
357.325 |
| Metro |
2 |
0.029 |
0.014 |
0.004 |
3.326 |
| Metro |
5 |
0.038 |
0.014 |
0.002 |
10.967 |
| Metro |
10 |
0.056 |
0.015 |
0.002 |
21.986 |
| Metro |
15 |
0.054 |
0.015 |
0.002 |
19.603 |
| Metro |
30 |
0.094 |
0.015 |
0.001 |
73.960 |
| DEMetro_Z |
2 |
0.041 |
0.014 |
0.004 |
6.014 |
| DEMetro_Z |
5 |
0.432 |
0.014 |
0.002 |
186.419 |
| DEMetro_Z |
10 |
0.471 |
0.015 |
0.002 |
243.808 |
| DEMetro_Z |
15 |
0.439 |
0.015 |
0.002 |
215.608 |
| DEMetro_Z |
30 |
0.481 |
0.015 |
0.001 |
436.952 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
R Hat (scatter)
Mode Transitions
One Chain results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
-0.049 |
0.961 |
-0.019 |
| HMC |
5 |
2.227 |
0.037 |
1.031 |
| HMC |
10 |
0.468 |
0.645 |
0.257 |
| HMC |
15 |
1.057 |
0.312 |
2.057 |
| HMC |
30 |
1.120 |
0.286 |
41.637 |
| SMC |
2 |
-1.612 |
0.124 |
-0.540 |
| SMC |
5 |
5.131 |
0.000216 |
5.773 |
| SMC |
10 |
5.326 |
0.000237 |
25.388 |
| SMC |
15 |
6.545 |
2.74e-05 |
9.025 |
| SMC |
30 |
11.888 |
7.84e-08 |
21.803 |
| Metro |
2 |
2.258 |
0.0435 |
3.234 |
| Metro |
5 |
1.312 |
0.216 |
11.876 |
| Metro |
10 |
2.778 |
0.0176 |
6.756 |
| Metro |
15 |
3.640 |
0.00157 |
1.725 |
| Metro |
30 |
1.817 |
0.0966 |
28.405 |
| DEMetro_Z |
2 |
1.868 |
0.0818 |
1.395 |
| DEMetro_Z |
5 |
2.712 |
0.0202 |
79.137 |
| DEMetro_Z |
10 |
4.503 |
0.000896 |
109.078 |
| DEMetro_Z |
15 |
7.240 |
1.65e-05 |
67.475 |
| DEMetro_Z |
30 |
12.859 |
5.69e-08 |
672.567 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
-1.700
|
0.117
|
-0.491
|
| HMC_vs_DEMetro_Z |
1
|
-2.672
|
0.0217
|
-0.771
|
| HMC_vs_DEMetro_Z |
2
|
-4.525
|
0.000864
|
-1.306
|
| HMC_vs_DEMetro_Z |
3
|
-8.224
|
5.02e-06
|
-2.374
|
| HMC_vs_DEMetro_Z |
4
|
-9.002
|
2.09e-06
|
-2.599
|
| Metro_vs_SMC |
0
|
2.675
|
0.0216
|
0.772
|
| Metro_vs_SMC |
1
|
0.673
|
0.515
|
0.194
|
| Metro_vs_SMC |
2
|
-3.768
|
0.00311
|
-1.088
|
| Metro_vs_SMC |
3
|
-5.525
|
0.000179
|
-1.595
|
| Metro_vs_SMC |
4
|
0.430
|
0.675
|
0.124
|
| Metro_vs_DEMetro_Z |
0
|
1.266
|
0.232
|
0.365
|
| Metro_vs_DEMetro_Z |
1
|
-2.081
|
0.0616
|
-0.601
|
| Metro_vs_DEMetro_Z |
2
|
-4.143
|
0.00164
|
-1.196
|
| Metro_vs_DEMetro_Z |
3
|
-7.012
|
2.23e-05
|
-2.024
|
| Metro_vs_DEMetro_Z |
4
|
-10.656
|
3.9e-07
|
-3.076
|
| HMC_vs_Metro |
0
|
-2.073
|
0.0625
|
-0.598
|
| HMC_vs_Metro |
1
|
-1.195
|
0.257
|
-0.345
|
| HMC_vs_Metro |
2
|
-2.499
|
0.0296
|
-0.721
|
| HMC_vs_Metro |
3
|
0.171
|
0.867
|
0.049
|
| HMC_vs_Metro |
4
|
0.313
|
0.76
|
0.090
|
| HMC_vs_SMC |
0
|
2.198
|
0.0503
|
0.634
|
| HMC_vs_SMC |
1
|
-4.785
|
0.000567
|
-1.381
|
| HMC_vs_SMC |
2
|
-5.080
|
0.000355
|
-1.466
|
| HMC_vs_SMC |
3
|
-6.759
|
3.12e-05
|
-1.951
|
| HMC_vs_SMC |
4
|
0.531
|
0.606
|
0.153
|
| DEMetro_Z_vs_SMC |
0
|
2.472
|
0.031
|
0.714
|
| DEMetro_Z_vs_SMC |
1
|
2.517
|
0.0286
|
0.727
|
| DEMetro_Z_vs_SMC |
2
|
3.265
|
0.00753
|
0.943
|
| DEMetro_Z_vs_SMC |
3
|
6.921
|
2.52e-05
|
1.998
|
| DEMetro_Z_vs_SMC |
4
|
12.426
|
8.12e-08
|
3.587
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.071 |
0.072 |
0.040 |
-0.019 |
| HMC |
5 |
0.077 |
0.053 |
0.023 |
1.031 |
| HMC |
10 |
0.068 |
0.065 |
0.015 |
0.257 |
| HMC |
15 |
0.139 |
0.073 |
0.032 |
2.057 |
| HMC |
30 |
0.406 |
0.066 |
0.008 |
41.637 |
| SMC |
2 |
0.050 |
0.072 |
0.040 |
-0.540 |
| SMC |
5 |
0.187 |
0.053 |
0.023 |
5.773 |
| SMC |
10 |
0.439 |
0.065 |
0.015 |
25.388 |
| SMC |
15 |
0.361 |
0.073 |
0.032 |
9.025 |
| SMC |
30 |
0.244 |
0.066 |
0.008 |
21.803 |
| Metro |
2 |
0.201 |
0.072 |
0.040 |
3.234 |
| Metro |
5 |
0.328 |
0.053 |
0.023 |
11.876 |
| Metro |
10 |
0.164 |
0.065 |
0.015 |
6.756 |
| Metro |
15 |
0.128 |
0.073 |
0.032 |
1.725 |
| Metro |
30 |
0.298 |
0.066 |
0.008 |
28.405 |
| DEMetro_Z |
2 |
0.128 |
0.072 |
0.040 |
1.395 |
| DEMetro_Z |
5 |
1.880 |
0.053 |
0.023 |
79.137 |
| DEMetro_Z |
10 |
1.671 |
0.065 |
0.015 |
109.078 |
| DEMetro_Z |
15 |
2.224 |
0.073 |
0.032 |
67.475 |
| DEMetro_Z |
30 |
5.566 |
0.066 |
0.008 |
672.567 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
-0.094 |
0.926 |
-0.036 |
| HMC |
5 |
0.636 |
0.534 |
0.428 |
| HMC |
10 |
1.671 |
0.117 |
1.426 |
| HMC |
15 |
0.930 |
0.372 |
5.238 |
| HMC |
30 |
0.995 |
0.341 |
12.800 |
| SMC |
2 |
-0.147 |
0.884 |
-0.057 |
| SMC |
5 |
1.407 |
0.175 |
0.700 |
| SMC |
10 |
5.983 |
6.97e-05 |
9.513 |
| SMC |
15 |
4.505 |
0.000417 |
1.418 |
| SMC |
30 |
27.495 |
8.28e-13 |
28.326 |
| Metro |
2 |
0.268 |
0.792 |
0.102 |
| Metro |
5 |
0.992 |
0.342 |
3.461 |
| Metro |
10 |
1.739 |
0.109 |
4.101 |
| Metro |
15 |
-1.452 |
0.173 |
-0.424 |
| Metro |
30 |
1.095 |
0.296 |
4.018 |
| DEMetro_Z |
2 |
-0.008 |
0.994 |
-0.003 |
| DEMetro_Z |
5 |
1.678 |
0.121 |
63.429 |
| DEMetro_Z |
10 |
1.856 |
0.0904 |
33.956 |
| DEMetro_Z |
15 |
2.316 |
0.0385 |
2.784 |
| DEMetro_Z |
30 |
6.910 |
2.52e-05 |
57.595 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
0.565
|
0.583
|
0.163
|
| HMC_vs_SMC |
1
|
-0.409
|
0.69
|
-0.118
|
| HMC_vs_SMC |
2
|
-4.123
|
0.00169
|
-1.190
|
| HMC_vs_SMC |
3
|
0.684
|
0.508
|
0.197
|
| HMC_vs_SMC |
4
|
-1.226
|
0.246
|
-0.354
|
| Metro_vs_DEMetro_Z |
0
|
1.055
|
0.314
|
0.305
|
| Metro_vs_DEMetro_Z |
1
|
-1.556
|
0.148
|
-0.449
|
| Metro_vs_DEMetro_Z |
2
|
-1.583
|
0.142
|
-0.457
|
| Metro_vs_DEMetro_Z |
3
|
-2.745
|
0.0191
|
-0.792
|
| Metro_vs_DEMetro_Z |
4
|
-5.132
|
0.000327
|
-1.481
|
| HMC_vs_Metro |
0
|
-1.666
|
0.124
|
-0.481
|
| HMC_vs_Metro |
1
|
-0.831
|
0.424
|
-0.240
|
| HMC_vs_Metro |
2
|
-1.085
|
0.301
|
-0.313
|
| HMC_vs_Metro |
3
|
1.007
|
0.336
|
0.291
|
| HMC_vs_Metro |
4
|
0.643
|
0.533
|
0.186
|
| HMC_vs_DEMetro_Z |
0
|
-0.806
|
0.438
|
-0.233
|
| HMC_vs_DEMetro_Z |
1
|
-1.677
|
0.122
|
-0.484
|
| HMC_vs_DEMetro_Z |
2
|
-1.780
|
0.103
|
-0.514
|
| HMC_vs_DEMetro_Z |
3
|
0.499
|
0.627
|
0.144
|
| HMC_vs_DEMetro_Z |
4
|
-2.692
|
0.021
|
-0.777
|
| Metro_vs_SMC |
0
|
1.685
|
0.12
|
0.487
|
| Metro_vs_SMC |
1
|
0.801
|
0.44
|
0.231
|
| Metro_vs_SMC |
2
|
-2.458
|
0.0318
|
-0.709
|
| Metro_vs_SMC |
3
|
-15.320
|
9.12e-09
|
-4.422
|
| Metro_vs_SMC |
4
|
-6.434
|
4.85e-05
|
-1.857
|
| DEMetro_Z_vs_SMC |
0
|
1.788
|
0.101
|
0.516
|
| DEMetro_Z_vs_SMC |
1
|
1.671
|
0.123
|
0.482
|
| DEMetro_Z_vs_SMC |
2
|
1.294
|
0.222
|
0.374
|
| DEMetro_Z_vs_SMC |
3
|
1.169
|
0.267
|
0.337
|
| DEMetro_Z_vs_SMC |
4
|
3.587
|
0.00427
|
1.035
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
8.229 |
8.779 |
15.112 |
-0.036 |
| HMC |
5 |
7.288 |
5.105 |
5.103 |
0.428 |
| HMC |
10 |
8.613 |
3.930 |
3.285 |
1.426 |
| HMC |
15 |
184.784 |
17.964 |
31.848 |
5.238 |
| HMC |
30 |
51.365 |
4.774 |
3.640 |
12.800 |
| SMC |
2 |
7.911 |
8.779 |
15.112 |
-0.057 |
| SMC |
5 |
8.675 |
5.105 |
5.103 |
0.700 |
| SMC |
10 |
35.178 |
3.930 |
3.285 |
9.513 |
| SMC |
15 |
63.136 |
17.964 |
31.848 |
1.418 |
| SMC |
30 |
107.877 |
4.774 |
3.640 |
28.326 |
| Metro |
2 |
10.328 |
8.779 |
15.112 |
0.102 |
| Metro |
5 |
22.769 |
5.105 |
5.103 |
3.461 |
| Metro |
10 |
17.401 |
3.930 |
3.285 |
4.101 |
| Metro |
15 |
4.464 |
17.964 |
31.848 |
-0.424 |
| Metro |
30 |
19.400 |
4.774 |
3.640 |
4.018 |
| DEMetro_Z |
2 |
8.731 |
8.779 |
15.112 |
-0.003 |
| DEMetro_Z |
5 |
328.793 |
5.105 |
5.103 |
63.429 |
| DEMetro_Z |
10 |
115.466 |
3.930 |
3.285 |
33.956 |
| DEMetro_Z |
15 |
106.630 |
17.964 |
31.848 |
2.784 |
| DEMetro_Z |
30 |
214.412 |
4.774 |
3.640 |
57.595 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
2.323 |
0.0301 |
0.878 |
| HMC |
5 |
1.968 |
0.074 |
4.678 |
| HMC |
10 |
3.218 |
0.00774 |
6.077 |
| HMC |
15 |
1.236 |
0.242 |
20.140 |
| HMC |
30 |
1.928 |
0.0801 |
47.470 |
| SMC |
2 |
0.246 |
0.808 |
0.112 |
| SMC |
5 |
5.312 |
0.000247 |
56.418 |
| SMC |
10 |
11.914 |
1.25e-07 |
229.026 |
| SMC |
15 |
24.403 |
5.56e-11 |
119.339 |
| SMC |
30 |
53.436 |
1.17e-14 |
559.479 |
| Metro |
2 |
2.903 |
0.0133 |
4.111 |
| Metro |
5 |
1.730 |
0.111 |
23.165 |
| Metro |
10 |
1.729 |
0.112 |
46.640 |
| Metro |
15 |
4.692 |
0.000185 |
2.658 |
| Metro |
30 |
1.604 |
0.137 |
68.286 |
| DEMetro_Z |
2 |
5.761 |
2.23e-05 |
3.438 |
| DEMetro_Z |
5 |
2.275 |
0.0439 |
288.225 |
| DEMetro_Z |
10 |
3.501 |
0.00496 |
300.782 |
| DEMetro_Z |
15 |
6.392 |
5.13e-05 |
137.818 |
| DEMetro_Z |
30 |
14.310 |
1.87e-08 |
815.183 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
0.432
|
0.674
|
0.125
|
| Metro_vs_DEMetro_Z |
1
|
-2.028
|
0.0675
|
-0.585
|
| Metro_vs_DEMetro_Z |
2
|
-2.693
|
0.0209
|
-0.777
|
| Metro_vs_DEMetro_Z |
3
|
-6.271
|
6.08e-05
|
-1.810
|
| Metro_vs_DEMetro_Z |
4
|
-8.602
|
3.26e-06
|
-2.483
|
| DEMetro_Z_vs_SMC |
0
|
6.504
|
4.4e-05
|
1.878
|
| DEMetro_Z_vs_SMC |
1
|
1.900
|
0.0839
|
0.549
|
| DEMetro_Z_vs_SMC |
2
|
0.741
|
0.474
|
0.214
|
| DEMetro_Z_vs_SMC |
3
|
0.831
|
0.424
|
0.240
|
| DEMetro_Z_vs_SMC |
4
|
4.721
|
0.000628
|
1.363
|
| HMC_vs_DEMetro_Z |
0
|
-6.247
|
6.28e-05
|
-1.803
|
| HMC_vs_DEMetro_Z |
1
|
-2.245
|
0.0463
|
-0.648
|
| HMC_vs_DEMetro_Z |
2
|
-3.448
|
0.00544
|
-0.995
|
| HMC_vs_DEMetro_Z |
3
|
-5.854
|
0.00011
|
-1.690
|
| HMC_vs_DEMetro_Z |
4
|
-11.973
|
1.19e-07
|
-3.456
|
| HMC_vs_Metro |
0
|
-2.195
|
0.0506
|
-0.634
|
| HMC_vs_Metro |
1
|
-1.303
|
0.219
|
-0.376
|
| HMC_vs_Metro |
2
|
-1.468
|
0.17
|
-0.424
|
| HMC_vs_Metro |
3
|
1.066
|
0.309
|
0.308
|
| HMC_vs_Metro |
4
|
-0.433
|
0.673
|
-0.125
|
| HMC_vs_SMC |
0
|
1.904
|
0.0833
|
0.550
|
| HMC_vs_SMC |
1
|
-4.846
|
0.000514
|
-1.399
|
| HMC_vs_SMC |
2
|
-10.709
|
3.71e-07
|
-3.091
|
| HMC_vs_SMC |
3
|
-6.217
|
6.56e-05
|
-1.795
|
| HMC_vs_SMC |
4
|
-19.649
|
6.46e-10
|
-5.672
|
| Metro_vs_SMC |
0
|
3.022
|
0.0116
|
0.872
|
| Metro_vs_SMC |
1
|
-2.015
|
0.069
|
-0.582
|
| Metro_vs_SMC |
2
|
-6.669
|
3.52e-05
|
-1.925
|
| Metro_vs_SMC |
3
|
-23.081
|
1.14e-10
|
-6.663
|
| Metro_vs_SMC |
4
|
-11.185
|
2.39e-07
|
-3.229
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.155 |
0.122 |
0.038 |
0.878 |
| HMC |
5 |
0.184 |
0.113 |
0.015 |
4.678 |
| HMC |
10 |
0.190 |
0.110 |
0.013 |
6.077 |
| HMC |
15 |
0.919 |
0.131 |
0.039 |
20.140 |
| HMC |
30 |
0.690 |
0.111 |
0.012 |
47.470 |
| SMC |
2 |
0.126 |
0.122 |
0.038 |
0.112 |
| SMC |
5 |
0.977 |
0.113 |
0.015 |
56.418 |
| SMC |
10 |
3.127 |
0.110 |
0.013 |
229.026 |
| SMC |
15 |
4.797 |
0.131 |
0.039 |
119.339 |
| SMC |
30 |
6.941 |
0.111 |
0.012 |
559.479 |
| Metro |
2 |
0.277 |
0.122 |
0.038 |
4.111 |
| Metro |
5 |
0.467 |
0.113 |
0.015 |
23.165 |
| Metro |
10 |
0.724 |
0.110 |
0.013 |
46.640 |
| Metro |
15 |
0.235 |
0.131 |
0.039 |
2.658 |
| Metro |
30 |
0.944 |
0.111 |
0.012 |
68.286 |
| DEMetro_Z |
2 |
0.252 |
0.122 |
0.038 |
3.438 |
| DEMetro_Z |
5 |
4.527 |
0.113 |
0.015 |
288.225 |
| DEMetro_Z |
10 |
4.073 |
0.110 |
0.013 |
300.782 |
| DEMetro_Z |
15 |
5.519 |
0.131 |
0.039 |
137.818 |
| DEMetro_Z |
30 |
10.063 |
0.111 |
0.012 |
815.183 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
2.821 |
0.0108 |
1.464 |
| HMC |
5 |
2.660 |
0.021 |
3.910 |
| HMC |
10 |
3.393 |
0.00567 |
6.776 |
| HMC |
15 |
1.663 |
0.125 |
45.702 |
| HMC |
30 |
1.491 |
0.164 |
94.461 |
| SMC |
2 |
1.066 |
0.298 |
0.430 |
| SMC |
5 |
8.612 |
3.18e-06 |
78.216 |
| SMC |
10 |
30.707 |
4.72e-12 |
183.841 |
| SMC |
15 |
65.692 |
7.54e-16 |
197.930 |
| SMC |
30 |
109.737 |
2.68e-18 |
361.030 |
| Metro |
2 |
3.972 |
0.00146 |
3.470 |
| Metro |
5 |
5.067 |
0.000335 |
13.032 |
| Metro |
10 |
2.407 |
0.0348 |
40.912 |
| Metro |
15 |
5.701 |
0.000127 |
15.900 |
| Metro |
30 |
3.482 |
0.00513 |
93.183 |
| DEMetro_Z |
2 |
5.634 |
6.15e-05 |
4.648 |
| DEMetro_Z |
5 |
4.050 |
0.00192 |
95.843 |
| DEMetro_Z |
10 |
11.356 |
2.04e-07 |
210.000 |
| DEMetro_Z |
15 |
18.313 |
1.35e-09 |
233.670 |
| DEMetro_Z |
30 |
40.536 |
2.44e-13 |
493.180 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
4.656
|
0.000698
|
1.344
|
| DEMetro_Z_vs_SMC |
1
|
0.704
|
0.496
|
0.203
|
| DEMetro_Z_vs_SMC |
2
|
1.273
|
0.229
|
0.367
|
| DEMetro_Z_vs_SMC |
3
|
2.835
|
0.0162
|
0.818
|
| DEMetro_Z_vs_SMC |
4
|
11.051
|
2.7e-07
|
3.190
|
| HMC_vs_Metro |
0
|
-1.994
|
0.0715
|
-0.576
|
| HMC_vs_Metro |
1
|
-2.700
|
0.0207
|
-0.779
|
| HMC_vs_Metro |
2
|
-1.961
|
0.0757
|
-0.566
|
| HMC_vs_Metro |
3
|
1.048
|
0.317
|
0.303
|
| HMC_vs_Metro |
4
|
0.019
|
0.985
|
0.005
|
| Metro_vs_DEMetro_Z |
0
|
-1.082
|
0.302
|
-0.312
|
| Metro_vs_DEMetro_Z |
1
|
-3.257
|
0.00765
|
-0.940
|
| Metro_vs_DEMetro_Z |
2
|
-6.188
|
6.83e-05
|
-1.786
|
| Metro_vs_DEMetro_Z |
3
|
-17.412
|
2.35e-09
|
-5.026
|
| Metro_vs_DEMetro_Z |
4
|
-13.006
|
5.07e-08
|
-3.754
|
| HMC_vs_SMC |
0
|
1.768
|
0.105
|
0.510
|
| HMC_vs_SMC |
1
|
-8.235
|
4.96e-06
|
-2.377
|
| HMC_vs_SMC |
2
|
-24.045
|
7.35e-11
|
-6.941
|
| HMC_vs_SMC |
3
|
-5.936
|
9.78e-05
|
-1.714
|
| HMC_vs_SMC |
4
|
-4.139
|
0.00165
|
-1.195
|
| Metro_vs_SMC |
0
|
3.750
|
0.00321
|
1.083
|
| Metro_vs_SMC |
1
|
-7.319
|
1.51e-05
|
-2.113
|
| Metro_vs_SMC |
2
|
-8.592
|
3.29e-06
|
-2.480
|
| Metro_vs_SMC |
3
|
-37.942
|
5.15e-13
|
-10.953
|
| Metro_vs_SMC |
4
|
-10.177
|
6.2e-07
|
-2.938
|
| HMC_vs_DEMetro_Z |
0
|
-4.266
|
0.00133
|
-1.232
|
| HMC_vs_DEMetro_Z |
1
|
-3.864
|
0.00263
|
-1.116
|
| HMC_vs_DEMetro_Z |
2
|
-10.650
|
3.93e-07
|
-3.074
|
| HMC_vs_DEMetro_Z |
3
|
-6.819
|
2.88e-05
|
-1.968
|
| HMC_vs_DEMetro_Z |
4
|
-5.897
|
0.000104
|
-1.702
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.021 |
0.014 |
0.004 |
1.464 |
| HMC |
5 |
0.023 |
0.014 |
0.002 |
3.910 |
| HMC |
10 |
0.027 |
0.015 |
0.002 |
6.776 |
| HMC |
15 |
0.105 |
0.015 |
0.002 |
45.702 |
| HMC |
30 |
0.116 |
0.015 |
0.001 |
94.461 |
| SMC |
2 |
0.016 |
0.014 |
0.004 |
0.430 |
| SMC |
5 |
0.189 |
0.014 |
0.002 |
78.216 |
| SMC |
10 |
0.359 |
0.015 |
0.002 |
183.841 |
| SMC |
15 |
0.404 |
0.015 |
0.002 |
197.930 |
| SMC |
30 |
0.400 |
0.015 |
0.001 |
361.030 |
| Metro |
2 |
0.030 |
0.014 |
0.004 |
3.470 |
| Metro |
5 |
0.043 |
0.014 |
0.002 |
13.032 |
| Metro |
10 |
0.091 |
0.015 |
0.002 |
40.912 |
| Metro |
15 |
0.046 |
0.015 |
0.002 |
15.900 |
| Metro |
30 |
0.114 |
0.015 |
0.001 |
93.183 |
| DEMetro_Z |
2 |
0.035 |
0.014 |
0.004 |
4.648 |
| DEMetro_Z |
5 |
0.229 |
0.014 |
0.002 |
95.843 |
| DEMetro_Z |
10 |
0.408 |
0.015 |
0.002 |
210.000 |
| DEMetro_Z |
15 |
0.474 |
0.015 |
0.002 |
233.670 |
| DEMetro_Z |
30 |
0.541 |
0.015 |
0.001 |
493.180 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
Mode Transitions
KDE + Init Plots
Forest & Ridge Plots
Pooled
Chain
Pairwise Scatter Plots
Pooled
Chain
Vary_Dimension_with_high_Multimodality
(Mixture,
dimension,
12 runs)
Pooled Chains results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
5.562 |
0.000167 |
37.881 |
| HMC |
5 |
4.958 |
0.000427 |
44.824 |
| HMC |
10 |
4.037 |
0.00195 |
39.000 |
| HMC |
15 |
2.944 |
0.0133 |
27.382 |
| HMC |
30 |
3.871 |
0.00259 |
36.281 |
| SMC |
2 |
1.308 |
0.209 |
0.428 |
| SMC |
5 |
-0.281 |
0.781 |
-0.100 |
| SMC |
10 |
0.039 |
0.969 |
0.019 |
| SMC |
15 |
-0.206 |
0.839 |
-0.072 |
| SMC |
30 |
0.207 |
0.838 |
0.084 |
| Metro |
2 |
3.929 |
0.00234 |
27.906 |
| Metro |
5 |
3.295 |
0.00713 |
36.863 |
| Metro |
10 |
5.658 |
0.000145 |
35.901 |
| Metro |
15 |
4.112 |
0.00171 |
27.857 |
| Metro |
30 |
3.742 |
0.00324 |
31.482 |
| DEMetro_Z |
2 |
5.620 |
0.000153 |
32.678 |
| DEMetro_Z |
5 |
7.251 |
1.64e-05 |
105.668 |
| DEMetro_Z |
10 |
11.875 |
1.29e-07 |
300.941 |
| DEMetro_Z |
15 |
21.980 |
1.92e-10 |
358.927 |
| DEMetro_Z |
30 |
30.726 |
5.08e-12 |
529.976 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
0.543
|
0.598
|
0.157
|
| HMC_vs_DEMetro_Z |
1
|
-3.001
|
0.0121
|
-0.866
|
| HMC_vs_DEMetro_Z |
2
|
-9.738
|
9.63e-07
|
-2.811
|
| HMC_vs_DEMetro_Z |
3
|
-19.893
|
5.66e-10
|
-5.743
|
| HMC_vs_DEMetro_Z |
4
|
-27.201
|
1.93e-11
|
-7.852
|
| Metro_vs_SMC |
0
|
3.861
|
0.00265
|
1.115
|
| Metro_vs_SMC |
1
|
3.301
|
0.00707
|
0.953
|
| Metro_vs_SMC |
2
|
5.662
|
0.000146
|
1.634
|
| Metro_vs_SMC |
3
|
4.192
|
0.00151
|
1.210
|
| Metro_vs_SMC |
4
|
3.757
|
0.00317
|
1.085
|
| Metro_vs_DEMetro_Z |
0
|
-0.481
|
0.64
|
-0.139
|
| Metro_vs_DEMetro_Z |
1
|
-3.252
|
0.00771
|
-0.939
|
| Metro_vs_DEMetro_Z |
2
|
-10.545
|
4.34e-07
|
-3.044
|
| Metro_vs_DEMetro_Z |
3
|
-18.875
|
9.94e-10
|
-5.449
|
| Metro_vs_DEMetro_Z |
4
|
-27.077
|
2.03e-11
|
-7.816
|
| HMC_vs_Metro |
0
|
2.321
|
0.0405
|
0.670
|
| HMC_vs_Metro |
1
|
0.756
|
0.466
|
0.218
|
| HMC_vs_Metro |
2
|
0.347
|
0.735
|
0.100
|
| HMC_vs_Metro |
3
|
-0.040
|
0.969
|
-0.011
|
| HMC_vs_Metro |
4
|
1.568
|
0.145
|
0.453
|
| HMC_vs_SMC |
0
|
5.510
|
0.000183
|
1.591
|
| HMC_vs_SMC |
1
|
4.953
|
0.000434
|
1.430
|
| HMC_vs_SMC |
2
|
4.064
|
0.00187
|
1.173
|
| HMC_vs_SMC |
3
|
2.932
|
0.0136
|
0.846
|
| HMC_vs_SMC |
4
|
3.890
|
0.00252
|
1.123
|
| DEMetro_Z_vs_SMC |
0
|
5.577
|
0.000166
|
1.610
|
| DEMetro_Z_vs_SMC |
1
|
7.247
|
1.65e-05
|
2.092
|
| DEMetro_Z_vs_SMC |
2
|
11.851
|
1.32e-07
|
3.421
|
| DEMetro_Z_vs_SMC |
3
|
21.999
|
1.92e-10
|
6.350
|
| DEMetro_Z_vs_SMC |
4
|
30.598
|
5.38e-12
|
8.833
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
2.280 |
0.095 |
0.058 |
37.881 |
| HMC |
5 |
1.132 |
0.042 |
0.024 |
44.824 |
| HMC |
10 |
0.717 |
0.039 |
0.017 |
39.000 |
| HMC |
15 |
0.467 |
0.034 |
0.016 |
27.382 |
| HMC |
30 |
0.466 |
0.034 |
0.012 |
36.281 |
| SMC |
2 |
0.120 |
0.095 |
0.058 |
0.428 |
| SMC |
5 |
0.039 |
0.042 |
0.024 |
-0.100 |
| SMC |
10 |
0.039 |
0.039 |
0.017 |
0.019 |
| SMC |
15 |
0.033 |
0.034 |
0.016 |
-0.072 |
| SMC |
30 |
0.035 |
0.034 |
0.012 |
0.084 |
| Metro |
2 |
1.704 |
0.095 |
0.058 |
27.906 |
| Metro |
5 |
0.939 |
0.042 |
0.024 |
36.863 |
| Metro |
10 |
0.663 |
0.039 |
0.017 |
35.901 |
| Metro |
15 |
0.475 |
0.034 |
0.016 |
27.857 |
| Metro |
30 |
0.408 |
0.034 |
0.012 |
31.482 |
| DEMetro_Z |
2 |
1.980 |
0.095 |
0.058 |
32.678 |
| DEMetro_Z |
5 |
2.613 |
0.042 |
0.024 |
105.668 |
| DEMetro_Z |
10 |
5.272 |
0.039 |
0.017 |
300.941 |
| DEMetro_Z |
15 |
5.708 |
0.034 |
0.016 |
358.927 |
| DEMetro_Z |
30 |
6.343 |
0.034 |
0.012 |
529.976 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
3.631 |
0.00395 |
72.487 |
| HMC |
5 |
3.279 |
0.00735 |
79.857 |
| HMC |
10 |
2.898 |
0.0145 |
53.338 |
| HMC |
15 |
2.269 |
0.0444 |
93.577 |
| HMC |
30 |
2.865 |
0.0154 |
118.048 |
| SMC |
2 |
0.448 |
0.659 |
0.185 |
| SMC |
5 |
1.320 |
0.203 |
0.699 |
| SMC |
10 |
1.224 |
0.236 |
0.645 |
| SMC |
15 |
1.055 |
0.307 |
0.672 |
| SMC |
30 |
1.416 |
0.177 |
1.027 |
| Metro |
2 |
2.722 |
0.0199 |
51.092 |
| Metro |
5 |
2.434 |
0.0332 |
75.186 |
| Metro |
10 |
5.400 |
0.000214 |
38.220 |
| Metro |
15 |
3.973 |
0.00218 |
71.717 |
| Metro |
30 |
2.726 |
0.0197 |
93.961 |
| DEMetro_Z |
2 |
3.246 |
0.00779 |
50.136 |
| DEMetro_Z |
5 |
8.060 |
6.08e-06 |
792.552 |
| DEMetro_Z |
10 |
12.795 |
6e-08 |
2385.081 |
| DEMetro_Z |
15 |
11.806 |
1.38e-07 |
7355.687 |
| DEMetro_Z |
30 |
24.527 |
5.93e-11 |
10924.805 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
3.652
|
0.00381
|
1.054
|
| HMC_vs_SMC |
1
|
3.261
|
0.00758
|
0.941
|
| HMC_vs_SMC |
2
|
2.887
|
0.0148
|
0.833
|
| HMC_vs_SMC |
3
|
2.274
|
0.044
|
0.656
|
| HMC_vs_SMC |
4
|
2.826
|
0.0165
|
0.816
|
| Metro_vs_DEMetro_Z |
0
|
0.039
|
0.97
|
0.011
|
| Metro_vs_DEMetro_Z |
1
|
-6.453
|
4.72e-05
|
-1.863
|
| Metro_vs_DEMetro_Z |
2
|
-12.544
|
7.36e-08
|
-3.621
|
| Metro_vs_DEMetro_Z |
3
|
-11.841
|
1.33e-07
|
-3.418
|
| Metro_vs_DEMetro_Z |
4
|
-25.011
|
4.8e-11
|
-7.220
|
| HMC_vs_Metro |
0
|
1.812
|
0.0973
|
0.523
|
| HMC_vs_Metro |
1
|
0.174
|
0.865
|
0.050
|
| HMC_vs_Metro |
2
|
0.842
|
0.418
|
0.243
|
| HMC_vs_Metro |
3
|
0.477
|
0.643
|
0.138
|
| HMC_vs_Metro |
4
|
1.469
|
0.17
|
0.424
|
| HMC_vs_DEMetro_Z |
0
|
0.834
|
0.422
|
0.241
|
| HMC_vs_DEMetro_Z |
1
|
-6.556
|
4.1e-05
|
-1.892
|
| HMC_vs_DEMetro_Z |
2
|
-12.635
|
6.84e-08
|
-3.647
|
| HMC_vs_DEMetro_Z |
3
|
-11.653
|
1.57e-07
|
-3.364
|
| HMC_vs_DEMetro_Z |
4
|
-24.936
|
4.96e-11
|
-7.198
|
| Metro_vs_SMC |
0
|
2.738
|
0.0193
|
0.790
|
| Metro_vs_SMC |
1
|
2.406
|
0.0349
|
0.694
|
| Metro_vs_SMC |
2
|
5.242
|
0.000276
|
1.513
|
| Metro_vs_SMC |
3
|
3.882
|
0.00256
|
1.121
|
| Metro_vs_SMC |
4
|
2.682
|
0.0213
|
0.774
|
| DEMetro_Z_vs_SMC |
0
|
3.224
|
0.00811
|
0.931
|
| DEMetro_Z_vs_SMC |
1
|
8.033
|
6.28e-06
|
2.319
|
| DEMetro_Z_vs_SMC |
2
|
12.812
|
5.92e-08
|
3.699
|
| DEMetro_Z_vs_SMC |
3
|
11.804
|
1.38e-07
|
3.408
|
| DEMetro_Z_vs_SMC |
4
|
24.513
|
5.97e-11
|
7.076
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
10.111 |
0.155 |
0.137 |
72.487 |
| HMC |
5 |
4.029 |
0.076 |
0.049 |
79.857 |
| HMC |
10 |
2.612 |
0.072 |
0.048 |
53.338 |
| HMC |
15 |
1.776 |
0.049 |
0.018 |
93.577 |
| HMC |
30 |
1.932 |
0.045 |
0.016 |
118.048 |
| SMC |
2 |
0.181 |
0.155 |
0.137 |
0.185 |
| SMC |
5 |
0.111 |
0.076 |
0.049 |
0.699 |
| SMC |
10 |
0.102 |
0.072 |
0.048 |
0.645 |
| SMC |
15 |
0.062 |
0.049 |
0.018 |
0.672 |
| SMC |
30 |
0.062 |
0.045 |
0.016 |
1.027 |
| Metro |
2 |
7.172 |
0.155 |
0.137 |
51.092 |
| Metro |
5 |
3.798 |
0.076 |
0.049 |
75.186 |
| Metro |
10 |
1.892 |
0.072 |
0.048 |
38.220 |
| Metro |
15 |
1.373 |
0.049 |
0.018 |
71.717 |
| Metro |
30 |
1.547 |
0.045 |
0.016 |
93.961 |
| DEMetro_Z |
2 |
7.041 |
0.155 |
0.137 |
50.136 |
| DEMetro_Z |
5 |
39.304 |
0.076 |
0.049 |
792.552 |
| DEMetro_Z |
10 |
113.685 |
0.072 |
0.048 |
2385.081 |
| DEMetro_Z |
15 |
135.775 |
0.049 |
0.018 |
7355.687 |
| DEMetro_Z |
30 |
174.604 |
0.045 |
0.016 |
10924.805 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
5.550 |
0.000171 |
44.342 |
| HMC |
5 |
4.639 |
0.000716 |
55.077 |
| HMC |
10 |
4.134 |
0.00166 |
46.634 |
| HMC |
15 |
3.032 |
0.0114 |
33.803 |
| HMC |
30 |
3.935 |
0.00233 |
51.009 |
| SMC |
2 |
1.233 |
0.233 |
0.420 |
| SMC |
5 |
0.043 |
0.966 |
0.015 |
| SMC |
10 |
0.013 |
0.99 |
0.006 |
| SMC |
15 |
-0.119 |
0.907 |
-0.042 |
| SMC |
30 |
0.499 |
0.623 |
0.209 |
| Metro |
2 |
3.983 |
0.00214 |
31.010 |
| Metro |
5 |
3.382 |
0.00611 |
42.894 |
| Metro |
10 |
5.684 |
0.00014 |
43.846 |
| Metro |
15 |
4.142 |
0.00163 |
32.264 |
| Metro |
30 |
3.744 |
0.00324 |
44.373 |
| DEMetro_Z |
2 |
5.826 |
0.000113 |
39.832 |
| DEMetro_Z |
5 |
10.917 |
3.04e-07 |
205.510 |
| DEMetro_Z |
10 |
20.093 |
5.07e-10 |
640.960 |
| DEMetro_Z |
15 |
23.250 |
1.05e-10 |
800.436 |
| DEMetro_Z |
30 |
47.094 |
4.83e-14 |
1513.216 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
-0.792
|
0.445
|
-0.229
|
| Metro_vs_DEMetro_Z |
1
|
-6.524
|
4.29e-05
|
-1.883
|
| Metro_vs_DEMetro_Z |
2
|
-18.466
|
1.26e-09
|
-5.331
|
| Metro_vs_DEMetro_Z |
3
|
-24.502
|
5.99e-11
|
-7.073
|
| Metro_vs_DEMetro_Z |
4
|
-51.866
|
1.68e-14
|
-14.972
|
| DEMetro_Z_vs_SMC |
0
|
5.804
|
0.000119
|
1.676
|
| DEMetro_Z_vs_SMC |
1
|
10.896
|
3.12e-07
|
3.145
|
| DEMetro_Z_vs_SMC |
2
|
20.112
|
5.03e-10
|
5.806
|
| DEMetro_Z_vs_SMC |
3
|
23.315
|
1.03e-10
|
6.730
|
| DEMetro_Z_vs_SMC |
4
|
46.912
|
5.06e-14
|
13.542
|
| HMC_vs_DEMetro_Z |
0
|
0.397
|
0.699
|
0.115
|
| HMC_vs_DEMetro_Z |
1
|
-5.730
|
0.000132
|
-1.654
|
| HMC_vs_DEMetro_Z |
2
|
-18.681
|
1.11e-09
|
-5.393
|
| HMC_vs_DEMetro_Z |
3
|
-21.232
|
2.81e-10
|
-6.129
|
| HMC_vs_DEMetro_Z |
4
|
-50.336
|
2.34e-14
|
-14.531
|
| HMC_vs_Metro |
0
|
2.921
|
0.0139
|
0.843
|
| HMC_vs_Metro |
1
|
1.014
|
0.333
|
0.293
|
| HMC_vs_Metro |
2
|
0.253
|
0.805
|
0.073
|
| HMC_vs_Metro |
3
|
0.108
|
0.916
|
0.031
|
| HMC_vs_Metro |
4
|
1.681
|
0.121
|
0.485
|
| HMC_vs_SMC |
0
|
5.512
|
0.000183
|
1.591
|
| HMC_vs_SMC |
1
|
4.654
|
0.000701
|
1.343
|
| HMC_vs_SMC |
2
|
4.162
|
0.00159
|
1.201
|
| HMC_vs_SMC |
3
|
3.019
|
0.0117
|
0.871
|
| HMC_vs_SMC |
4
|
3.933
|
0.00234
|
1.135
|
| Metro_vs_SMC |
0
|
3.923
|
0.00238
|
1.132
|
| Metro_vs_SMC |
1
|
3.374
|
0.00621
|
0.974
|
| Metro_vs_SMC |
2
|
5.663
|
0.000146
|
1.635
|
| Metro_vs_SMC |
3
|
4.216
|
0.00145
|
1.217
|
| Metro_vs_SMC |
4
|
3.743
|
0.00325
|
1.081
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
2.073 |
0.103 |
0.044 |
44.342 |
| HMC |
5 |
0.968 |
0.051 |
0.017 |
55.077 |
| HMC |
10 |
0.592 |
0.047 |
0.012 |
46.634 |
| HMC |
15 |
0.396 |
0.042 |
0.010 |
33.803 |
| HMC |
30 |
0.375 |
0.040 |
0.007 |
51.009 |
| SMC |
2 |
0.121 |
0.103 |
0.044 |
0.420 |
| SMC |
5 |
0.051 |
0.051 |
0.017 |
0.015 |
| SMC |
10 |
0.047 |
0.047 |
0.012 |
0.006 |
| SMC |
15 |
0.042 |
0.042 |
0.010 |
-0.042 |
| SMC |
30 |
0.041 |
0.040 |
0.007 |
0.209 |
| Metro |
2 |
1.481 |
0.103 |
0.044 |
31.010 |
| Metro |
5 |
0.765 |
0.051 |
0.017 |
42.894 |
| Metro |
10 |
0.560 |
0.047 |
0.012 |
43.846 |
| Metro |
15 |
0.380 |
0.042 |
0.010 |
32.264 |
| Metro |
30 |
0.332 |
0.040 |
0.007 |
44.373 |
| DEMetro_Z |
2 |
1.873 |
0.103 |
0.044 |
39.832 |
| DEMetro_Z |
5 |
3.473 |
0.051 |
0.017 |
205.510 |
| DEMetro_Z |
10 |
7.536 |
0.047 |
0.012 |
640.960 |
| DEMetro_Z |
15 |
8.424 |
0.042 |
0.010 |
800.436 |
| DEMetro_Z |
30 |
9.988 |
0.040 |
0.007 |
1513.216 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
5.687 |
0.00014 |
46.414 |
| HMC |
5 |
5.057 |
0.000366 |
57.530 |
| HMC |
10 |
3.992 |
0.00211 |
44.174 |
| HMC |
15 |
2.999 |
0.0121 |
33.721 |
| HMC |
30 |
3.831 |
0.00278 |
42.315 |
| SMC |
2 |
1.388 |
0.182 |
0.472 |
| SMC |
5 |
0.165 |
0.871 |
0.059 |
| SMC |
10 |
0.050 |
0.961 |
0.023 |
| SMC |
15 |
0.065 |
0.949 |
0.023 |
| SMC |
30 |
0.581 |
0.567 |
0.229 |
| Metro |
2 |
4.144 |
0.00162 |
34.573 |
| Metro |
5 |
3.313 |
0.00691 |
47.884 |
| Metro |
10 |
5.740 |
0.000129 |
40.348 |
| Metro |
15 |
4.136 |
0.00165 |
35.423 |
| Metro |
30 |
3.655 |
0.00378 |
35.644 |
| DEMetro_Z |
2 |
5.760 |
0.000125 |
40.101 |
| DEMetro_Z |
5 |
16.837 |
3.14e-09 |
96.979 |
| DEMetro_Z |
10 |
34.443 |
1.12e-12 |
120.856 |
| DEMetro_Z |
15 |
59.514 |
1.53e-15 |
133.908 |
| DEMetro_Z |
30 |
49.086 |
1.68e-14 |
128.307 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
5.730
|
0.000132
|
1.654
|
| DEMetro_Z_vs_SMC |
1
|
16.759
|
3.53e-09
|
4.838
|
| DEMetro_Z_vs_SMC |
2
|
33.508
|
2e-12
|
9.673
|
| DEMetro_Z_vs_SMC |
3
|
58.125
|
4.83e-15
|
16.779
|
| DEMetro_Z_vs_SMC |
4
|
48.162
|
3.79e-14
|
13.903
|
| HMC_vs_Metro |
0
|
2.383
|
0.0363
|
0.688
|
| HMC_vs_Metro |
1
|
0.687
|
0.506
|
0.198
|
| HMC_vs_Metro |
2
|
0.376
|
0.714
|
0.108
|
| HMC_vs_Metro |
3
|
-0.115
|
0.91
|
-0.033
|
| HMC_vs_Metro |
4
|
1.748
|
0.108
|
0.505
|
| Metro_vs_DEMetro_Z |
0
|
-0.465
|
0.651
|
-0.134
|
| Metro_vs_DEMetro_Z |
1
|
-2.829
|
0.0164
|
-0.817
|
| Metro_vs_DEMetro_Z |
2
|
-12.073
|
1.09e-07
|
-3.485
|
| Metro_vs_DEMetro_Z |
3
|
-10.946
|
2.98e-07
|
-3.160
|
| Metro_vs_DEMetro_Z |
4
|
-8.204
|
5.14e-06
|
-2.368
|
| HMC_vs_SMC |
0
|
5.620
|
0.000156
|
1.622
|
| HMC_vs_SMC |
1
|
5.052
|
0.000371
|
1.458
|
| HMC_vs_SMC |
2
|
4.012
|
0.00204
|
1.158
|
| HMC_vs_SMC |
3
|
2.977
|
0.0126
|
0.859
|
| HMC_vs_SMC |
4
|
3.836
|
0.00277
|
1.107
|
| Metro_vs_SMC |
0
|
4.072
|
0.00185
|
1.175
|
| Metro_vs_SMC |
1
|
3.299
|
0.00709
|
0.952
|
| Metro_vs_SMC |
2
|
5.733
|
0.000132
|
1.655
|
| Metro_vs_SMC |
3
|
4.198
|
0.00149
|
1.212
|
| Metro_vs_SMC |
4
|
3.652
|
0.00381
|
1.054
|
| HMC_vs_DEMetro_Z |
0
|
0.547
|
0.595
|
0.158
|
| HMC_vs_DEMetro_Z |
1
|
-2.639
|
0.023
|
-0.762
|
| HMC_vs_DEMetro_Z |
2
|
-7.204
|
1.74e-05
|
-2.080
|
| HMC_vs_DEMetro_Z |
3
|
-9.154
|
1.77e-06
|
-2.643
|
| HMC_vs_DEMetro_Z |
4
|
-6.907
|
2.56e-05
|
-1.994
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.344 |
0.014 |
0.007 |
46.414 |
| HMC |
5 |
0.256 |
0.010 |
0.004 |
57.530 |
| HMC |
10 |
0.216 |
0.012 |
0.005 |
44.174 |
| HMC |
15 |
0.157 |
0.012 |
0.004 |
33.721 |
| HMC |
30 |
0.195 |
0.015 |
0.004 |
42.315 |
| SMC |
2 |
0.017 |
0.014 |
0.007 |
0.472 |
| SMC |
5 |
0.010 |
0.010 |
0.004 |
0.059 |
| SMC |
10 |
0.012 |
0.012 |
0.005 |
0.023 |
| SMC |
15 |
0.012 |
0.012 |
0.004 |
0.023 |
| SMC |
30 |
0.016 |
0.015 |
0.004 |
0.229 |
| Metro |
2 |
0.260 |
0.014 |
0.007 |
34.573 |
| Metro |
5 |
0.214 |
0.010 |
0.004 |
47.884 |
| Metro |
10 |
0.198 |
0.012 |
0.005 |
40.348 |
| Metro |
15 |
0.164 |
0.012 |
0.004 |
35.423 |
| Metro |
30 |
0.167 |
0.015 |
0.004 |
35.644 |
| DEMetro_Z |
2 |
0.299 |
0.014 |
0.007 |
40.101 |
| DEMetro_Z |
5 |
0.424 |
0.010 |
0.004 |
96.979 |
| DEMetro_Z |
10 |
0.569 |
0.012 |
0.005 |
120.856 |
| DEMetro_Z |
15 |
0.586 |
0.012 |
0.004 |
133.908 |
| DEMetro_Z |
30 |
0.562 |
0.015 |
0.004 |
128.307 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
R Hat (scatter)
Mode Transitions
One Chain results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
163.377 |
6.13e-35 |
71.511 |
| HMC |
5 |
230.797 |
8.07e-37 |
108.686 |
| HMC |
10 |
202.744 |
3.18e-33 |
106.303 |
| HMC |
15 |
223.306 |
3.82e-38 |
95.636 |
| HMC |
30 |
187.937 |
8.89e-35 |
89.332 |
| SMC |
2 |
-1.177 |
0.252 |
-0.450 |
| SMC |
5 |
0.903 |
0.376 |
0.363 |
| SMC |
10 |
0.279 |
0.783 |
0.120 |
| SMC |
15 |
0.211 |
0.835 |
0.107 |
| SMC |
30 |
-1.069 |
0.299 |
-0.359 |
| Metro |
2 |
11.532 |
1.67e-07 |
65.765 |
| Metro |
5 |
225.837 |
4.02e-36 |
108.774 |
| Metro |
10 |
27.968 |
1.13e-11 |
101.457 |
| Metro |
15 |
8.017 |
6.33e-06 |
78.121 |
| Metro |
30 |
15.431 |
7.88e-09 |
83.880 |
| DEMetro_Z |
2 |
7.909 |
7.14e-06 |
59.034 |
| DEMetro_Z |
5 |
9.874 |
8.31e-07 |
120.739 |
| DEMetro_Z |
10 |
10.533 |
4.39e-07 |
529.331 |
| DEMetro_Z |
15 |
13.750 |
2.83e-08 |
587.025 |
| DEMetro_Z |
30 |
15.001 |
1.14e-08 |
916.835 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
1.643
|
0.129
|
0.474
|
| HMC_vs_DEMetro_Z |
1
|
-0.970
|
0.353
|
-0.280
|
| HMC_vs_DEMetro_Z |
2
|
-8.431
|
3.95e-06
|
-2.434
|
| HMC_vs_DEMetro_Z |
3
|
-11.518
|
1.77e-07
|
-3.325
|
| HMC_vs_DEMetro_Z |
4
|
-13.554
|
3.3e-08
|
-3.913
|
| Metro_vs_SMC |
0
|
11.517
|
1.77e-07
|
3.325
|
| Metro_vs_SMC |
1
|
182.977
|
1.63e-20
|
52.821
|
| Metro_vs_SMC |
2
|
28.360
|
1.23e-11
|
8.187
|
| Metro_vs_SMC |
3
|
8.080
|
5.94e-06
|
2.332
|
| Metro_vs_SMC |
4
|
15.248
|
9.59e-09
|
4.402
|
| Metro_vs_DEMetro_Z |
0
|
0.665
|
0.52
|
0.192
|
| Metro_vs_DEMetro_Z |
1
|
-0.958
|
0.359
|
-0.277
|
| Metro_vs_DEMetro_Z |
2
|
-8.477
|
3.75e-06
|
-2.447
|
| Metro_vs_DEMetro_Z |
3
|
-10.568
|
4.25e-07
|
-3.051
|
| Metro_vs_DEMetro_Z |
4
|
-13.351
|
3.86e-08
|
-3.854
|
| HMC_vs_Metro |
0
|
1.037
|
0.322
|
0.299
|
| HMC_vs_Metro |
1
|
-0.534
|
0.604
|
-0.154
|
| HMC_vs_Metro |
2
|
1.272
|
0.23
|
0.367
|
| HMC_vs_Metro |
3
|
1.803
|
0.0988
|
0.521
|
| HMC_vs_Metro |
4
|
0.998
|
0.34
|
0.288
|
| HMC_vs_SMC |
0
|
164.528
|
5.24e-20
|
47.495
|
| HMC_vs_SMC |
1
|
207.793
|
4.02e-21
|
59.985
|
| HMC_vs_SMC |
2
|
187.010
|
1.28e-20
|
53.985
|
| HMC_vs_SMC |
3
|
188.932
|
1.15e-20
|
54.540
|
| HMC_vs_SMC |
4
|
243.228
|
7.12e-22
|
70.214
|
| DEMetro_Z_vs_SMC |
0
|
7.966
|
6.8e-06
|
2.300
|
| DEMetro_Z_vs_SMC |
1
|
9.944
|
7.82e-07
|
2.871
|
| DEMetro_Z_vs_SMC |
2
|
10.522
|
4.44e-07
|
3.037
|
| DEMetro_Z_vs_SMC |
3
|
13.755
|
2.83e-08
|
3.971
|
| DEMetro_Z_vs_SMC |
4
|
15.011
|
1.13e-08
|
4.333
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
4.219 |
0.095 |
0.058 |
71.511 |
| HMC |
5 |
2.686 |
0.042 |
0.024 |
108.686 |
| HMC |
10 |
1.887 |
0.039 |
0.017 |
106.303 |
| HMC |
15 |
1.546 |
0.034 |
0.016 |
95.636 |
| HMC |
30 |
1.097 |
0.034 |
0.012 |
89.332 |
| SMC |
2 |
0.069 |
0.095 |
0.058 |
-0.450 |
| SMC |
5 |
0.051 |
0.042 |
0.024 |
0.363 |
| SMC |
10 |
0.041 |
0.039 |
0.017 |
0.120 |
| SMC |
15 |
0.036 |
0.034 |
0.016 |
0.107 |
| SMC |
30 |
0.029 |
0.034 |
0.012 |
-0.359 |
| Metro |
2 |
3.888 |
0.095 |
0.058 |
65.765 |
| Metro |
5 |
2.688 |
0.042 |
0.024 |
108.774 |
| Metro |
10 |
1.803 |
0.039 |
0.017 |
101.457 |
| Metro |
15 |
1.269 |
0.034 |
0.016 |
78.121 |
| Metro |
30 |
1.032 |
0.034 |
0.012 |
83.880 |
| DEMetro_Z |
2 |
3.500 |
0.095 |
0.058 |
59.034 |
| DEMetro_Z |
5 |
2.979 |
0.042 |
0.024 |
120.739 |
| DEMetro_Z |
10 |
9.243 |
0.039 |
0.017 |
529.331 |
| DEMetro_Z |
15 |
9.314 |
0.034 |
0.016 |
587.025 |
| DEMetro_Z |
30 |
10.949 |
0.034 |
0.012 |
916.835 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
481.407 |
5.24e-45 |
184.234 |
| HMC |
5 |
622.718 |
7.41e-43 |
322.788 |
| HMC |
10 |
426.026 |
8.57e-38 |
236.513 |
| HMC |
15 |
501.323 |
3.31e-29 |
502.037 |
| HMC |
30 |
568.515 |
4.16e-34 |
407.950 |
| SMC |
2 |
-0.722 |
0.479 |
-0.244 |
| SMC |
5 |
1.369 |
0.187 |
0.742 |
| SMC |
10 |
0.952 |
0.352 |
0.447 |
| SMC |
15 |
1.409 |
0.175 |
0.765 |
| SMC |
30 |
0.935 |
0.361 |
0.468 |
| Metro |
2 |
11.021 |
2.76e-07 |
168.967 |
| Metro |
5 |
567.035 |
2.47e-39 |
322.892 |
| Metro |
10 |
16.091 |
5.37e-09 |
217.214 |
| Metro |
15 |
6.926 |
2.5e-05 |
390.802 |
| Metro |
30 |
12.014 |
1.15e-07 |
376.857 |
| DEMetro_Z |
2 |
6.992 |
2.29e-05 |
146.368 |
| DEMetro_Z |
5 |
6.601 |
3.86e-05 |
375.216 |
| DEMetro_Z |
10 |
7.519 |
1.17e-05 |
653.238 |
| DEMetro_Z |
15 |
9.298 |
1.52e-06 |
1222.827 |
| DEMetro_Z |
30 |
11.250 |
2.25e-07 |
1195.056 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
504.010
|
2.36e-25
|
145.495
|
| HMC_vs_SMC |
1
|
422.811
|
1.63e-24
|
122.055
|
| HMC_vs_SMC |
2
|
291.200
|
9.83e-23
|
84.062
|
| HMC_vs_SMC |
3
|
560.746
|
7.29e-26
|
161.873
|
| HMC_vs_SMC |
4
|
491.438
|
3.11e-25
|
141.866
|
| Metro_vs_DEMetro_Z |
0
|
0.810
|
0.435
|
0.234
|
| Metro_vs_DEMetro_Z |
1
|
-0.918
|
0.378
|
-0.265
|
| Metro_vs_DEMetro_Z |
2
|
-5.203
|
0.000293
|
-1.502
|
| Metro_vs_DEMetro_Z |
3
|
-5.993
|
9.02e-05
|
-1.730
|
| Metro_vs_DEMetro_Z |
4
|
-7.751
|
8.81e-06
|
-2.237
|
| HMC_vs_Metro |
0
|
1.003
|
0.337
|
0.290
|
| HMC_vs_Metro |
1
|
-0.692
|
0.503
|
-0.200
|
| HMC_vs_Metro |
2
|
1.430
|
0.18
|
0.413
|
| HMC_vs_Metro |
3
|
1.960
|
0.0759
|
0.566
|
| HMC_vs_Metro |
4
|
0.992
|
0.343
|
0.286
|
| HMC_vs_DEMetro_Z |
0
|
1.802
|
0.099
|
0.520
|
| HMC_vs_DEMetro_Z |
1
|
-0.920
|
0.377
|
-0.266
|
| HMC_vs_DEMetro_Z |
2
|
-4.799
|
0.000555
|
-1.385
|
| HMC_vs_DEMetro_Z |
3
|
-5.475
|
0.000193
|
-1.580
|
| HMC_vs_DEMetro_Z |
4
|
-7.421
|
1.32e-05
|
-2.142
|
| Metro_vs_SMC |
0
|
10.994
|
2.85e-07
|
3.174
|
| Metro_vs_SMC |
1
|
398.993
|
3.08e-24
|
115.179
|
| Metro_vs_SMC |
2
|
15.996
|
5.78e-09
|
4.618
|
| Metro_vs_SMC |
3
|
6.893
|
2.61e-05
|
1.990
|
| Metro_vs_SMC |
4
|
12.033
|
1.13e-07
|
3.474
|
| DEMetro_Z_vs_SMC |
0
|
7.015
|
2.23e-05
|
2.025
|
| DEMetro_Z_vs_SMC |
1
|
6.577
|
3.98e-05
|
1.899
|
| DEMetro_Z_vs_SMC |
2
|
7.519
|
1.17e-05
|
2.170
|
| DEMetro_Z_vs_SMC |
3
|
9.274
|
1.56e-06
|
2.677
|
| DEMetro_Z_vs_SMC |
4
|
11.246
|
2.26e-07
|
3.246
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
25.458 |
0.155 |
0.137 |
184.234 |
| HMC |
5 |
16.053 |
0.076 |
0.049 |
322.788 |
| HMC |
10 |
11.338 |
0.072 |
0.048 |
236.513 |
| HMC |
15 |
9.313 |
0.049 |
0.018 |
502.037 |
| HMC |
30 |
6.564 |
0.045 |
0.016 |
407.950 |
| SMC |
2 |
0.122 |
0.155 |
0.137 |
-0.244 |
| SMC |
5 |
0.113 |
0.076 |
0.049 |
0.742 |
| SMC |
10 |
0.093 |
0.072 |
0.048 |
0.447 |
| SMC |
15 |
0.064 |
0.049 |
0.018 |
0.765 |
| SMC |
30 |
0.053 |
0.045 |
0.016 |
0.468 |
| Metro |
2 |
23.361 |
0.155 |
0.137 |
168.967 |
| Metro |
5 |
16.058 |
0.076 |
0.049 |
322.892 |
| Metro |
10 |
10.419 |
0.072 |
0.048 |
217.214 |
| Metro |
15 |
7.260 |
0.049 |
0.018 |
390.802 |
| Metro |
30 |
6.067 |
0.045 |
0.016 |
376.857 |
| DEMetro_Z |
2 |
20.258 |
0.155 |
0.137 |
146.368 |
| DEMetro_Z |
5 |
18.648 |
0.076 |
0.049 |
375.216 |
| DEMetro_Z |
10 |
31.189 |
0.072 |
0.048 |
653.238 |
| DEMetro_Z |
15 |
22.613 |
0.049 |
0.018 |
1222.827 |
| DEMetro_Z |
30 |
19.140 |
0.045 |
0.016 |
1195.056 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
50.013 |
5.7e-15 |
84.579 |
| HMC |
5 |
36.874 |
5.46e-13 |
139.193 |
| HMC |
10 |
42.934 |
8.6e-14 |
127.820 |
| HMC |
15 |
58.729 |
1.3e-15 |
113.994 |
| HMC |
30 |
57.603 |
2.22e-15 |
129.889 |
| SMC |
2 |
-1.248 |
0.226 |
-0.481 |
| SMC |
5 |
1.188 |
0.247 |
0.479 |
| SMC |
10 |
0.153 |
0.88 |
0.072 |
| SMC |
15 |
0.100 |
0.922 |
0.050 |
| SMC |
30 |
-1.092 |
0.288 |
-0.381 |
| Metro |
2 |
11.266 |
2.14e-07 |
75.901 |
| Metro |
5 |
32.421 |
2.35e-12 |
133.949 |
| Metro |
10 |
21.416 |
2.36e-10 |
121.809 |
| Metro |
15 |
8.027 |
6.27e-06 |
88.947 |
| Metro |
30 |
14.991 |
1.11e-08 |
121.766 |
| DEMetro_Z |
2 |
7.854 |
7.67e-06 |
68.105 |
| DEMetro_Z |
5 |
10.536 |
4.35e-07 |
153.753 |
| DEMetro_Z |
10 |
10.801 |
3.4e-07 |
694.859 |
| DEMetro_Z |
15 |
13.428 |
3.63e-08 |
738.282 |
| DEMetro_Z |
30 |
17.877 |
1.77e-09 |
1367.156 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
0.664
|
0.52
|
0.192
|
| Metro_vs_DEMetro_Z |
1
|
-1.362
|
0.201
|
-0.393
|
| Metro_vs_DEMetro_Z |
2
|
-9.067
|
1.95e-06
|
-2.618
|
| Metro_vs_DEMetro_Z |
3
|
-10.886
|
3.14e-07
|
-3.143
|
| Metro_vs_DEMetro_Z |
4
|
-15.900
|
6.16e-09
|
-4.590
|
| DEMetro_Z_vs_SMC |
0
|
7.925
|
7.14e-06
|
2.288
|
| DEMetro_Z_vs_SMC |
1
|
10.576
|
4.21e-07
|
3.053
|
| DEMetro_Z_vs_SMC |
2
|
10.793
|
3.43e-07
|
3.116
|
| DEMetro_Z_vs_SMC |
3
|
13.438
|
3.61e-08
|
3.879
|
| DEMetro_Z_vs_SMC |
4
|
17.883
|
1.77e-09
|
5.163
|
| HMC_vs_DEMetro_Z |
0
|
1.840
|
0.0929
|
0.531
|
| HMC_vs_DEMetro_Z |
1
|
-0.904
|
0.385
|
-0.261
|
| HMC_vs_DEMetro_Z |
2
|
-8.679
|
2.99e-06
|
-2.505
|
| HMC_vs_DEMetro_Z |
3
|
-11.217
|
2.32e-07
|
-3.238
|
| HMC_vs_DEMetro_Z |
4
|
-16.285
|
4.78e-09
|
-4.701
|
| HMC_vs_Metro |
0
|
1.294
|
0.222
|
0.373
|
| HMC_vs_Metro |
1
|
0.794
|
0.444
|
0.229
|
| HMC_vs_Metro |
2
|
0.910
|
0.383
|
0.263
|
| HMC_vs_Metro |
3
|
2.462
|
0.0316
|
0.711
|
| HMC_vs_Metro |
4
|
0.952
|
0.361
|
0.275
|
| HMC_vs_SMC |
0
|
48.787
|
3.29e-14
|
14.084
|
| HMC_vs_SMC |
1
|
36.589
|
7.66e-13
|
10.562
|
| HMC_vs_SMC |
2
|
41.453
|
1.96e-13
|
11.967
|
| HMC_vs_SMC |
3
|
56.657
|
6.39e-15
|
16.356
|
| HMC_vs_SMC |
4
|
60.742
|
2.98e-15
|
17.535
|
| Metro_vs_SMC |
0
|
11.195
|
2.37e-07
|
3.232
|
| Metro_vs_SMC |
1
|
32.952
|
2.4e-12
|
9.512
|
| Metro_vs_SMC |
2
|
21.543
|
2.4e-10
|
6.219
|
| Metro_vs_SMC |
3
|
8.108
|
5.75e-06
|
2.341
|
| Metro_vs_SMC |
4
|
14.872
|
1.25e-08
|
4.293
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
3.861 |
0.103 |
0.044 |
84.579 |
| HMC |
5 |
2.369 |
0.051 |
0.017 |
139.193 |
| HMC |
10 |
1.541 |
0.047 |
0.012 |
127.820 |
| HMC |
15 |
1.236 |
0.042 |
0.010 |
113.994 |
| HMC |
30 |
0.894 |
0.040 |
0.007 |
129.889 |
| SMC |
2 |
0.081 |
0.103 |
0.044 |
-0.481 |
| SMC |
5 |
0.059 |
0.051 |
0.017 |
0.479 |
| SMC |
10 |
0.048 |
0.047 |
0.012 |
0.072 |
| SMC |
15 |
0.043 |
0.042 |
0.010 |
0.050 |
| SMC |
30 |
0.037 |
0.040 |
0.007 |
-0.381 |
| Metro |
2 |
3.476 |
0.103 |
0.044 |
75.901 |
| Metro |
5 |
2.281 |
0.051 |
0.017 |
133.949 |
| Metro |
10 |
1.470 |
0.047 |
0.012 |
121.809 |
| Metro |
15 |
0.974 |
0.042 |
0.010 |
88.947 |
| Metro |
30 |
0.840 |
0.040 |
0.007 |
121.766 |
| DEMetro_Z |
2 |
3.129 |
0.103 |
0.044 |
68.105 |
| DEMetro_Z |
5 |
2.611 |
0.051 |
0.017 |
153.753 |
| DEMetro_Z |
10 |
8.165 |
0.047 |
0.012 |
694.859 |
| DEMetro_Z |
15 |
7.773 |
0.042 |
0.010 |
738.282 |
| DEMetro_Z |
30 |
9.028 |
0.040 |
0.007 |
1367.156 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
123.404 |
1.41e-24 |
85.157 |
| HMC |
5 |
110.285 |
9.46e-20 |
136.501 |
| HMC |
10 |
96.468 |
5.04e-19 |
119.952 |
| HMC |
15 |
125.378 |
1.53e-21 |
122.506 |
| HMC |
30 |
102.305 |
4.02e-20 |
105.081 |
| SMC |
2 |
-1.246 |
0.226 |
-0.481 |
| SMC |
5 |
1.650 |
0.113 |
0.672 |
| SMC |
10 |
0.175 |
0.863 |
0.075 |
| SMC |
15 |
0.172 |
0.865 |
0.094 |
| SMC |
30 |
-1.051 |
0.307 |
-0.355 |
| Metro |
2 |
11.405 |
1.89e-07 |
77.725 |
| Metro |
5 |
125.602 |
6.35e-21 |
138.199 |
| Metro |
10 |
25.519 |
3.34e-11 |
114.789 |
| Metro |
15 |
7.901 |
7.3e-06 |
98.956 |
| Metro |
30 |
15.066 |
1.04e-08 |
98.345 |
| DEMetro_Z |
2 |
8.072 |
5.91e-06 |
70.507 |
| DEMetro_Z |
5 |
16.298 |
4.56e-09 |
121.478 |
| DEMetro_Z |
10 |
29.701 |
6.86e-12 |
187.564 |
| DEMetro_Z |
15 |
39.041 |
3.28e-13 |
201.073 |
| DEMetro_Z |
30 |
33.209 |
2.03e-12 |
214.560 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
8.146
|
5.5e-06
|
2.351
|
| DEMetro_Z_vs_SMC |
1
|
16.097
|
5.41e-09
|
4.647
|
| DEMetro_Z_vs_SMC |
2
|
30.014
|
6.63e-12
|
8.664
|
| DEMetro_Z_vs_SMC |
3
|
39.106
|
3.7e-13
|
11.289
|
| DEMetro_Z_vs_SMC |
4
|
33.731
|
1.86e-12
|
9.737
|
| HMC_vs_Metro |
0
|
1.127
|
0.284
|
0.325
|
| HMC_vs_Metro |
1
|
-1.138
|
0.279
|
-0.329
|
| HMC_vs_Metro |
2
|
1.060
|
0.312
|
0.306
|
| HMC_vs_Metro |
3
|
1.857
|
0.0903
|
0.536
|
| HMC_vs_Metro |
4
|
0.960
|
0.358
|
0.277
|
| Metro_vs_DEMetro_Z |
0
|
0.609
|
0.555
|
0.176
|
| Metro_vs_DEMetro_Z |
1
|
2.196
|
0.0505
|
0.634
|
| Metro_vs_DEMetro_Z |
2
|
-8.796
|
2.62e-06
|
-2.539
|
| Metro_vs_DEMetro_Z |
3
|
-7.529
|
1.16e-05
|
-2.173
|
| Metro_vs_DEMetro_Z |
4
|
-12.368
|
8.52e-08
|
-3.570
|
| HMC_vs_SMC |
0
|
145.990
|
1.95e-19
|
42.144
|
| HMC_vs_SMC |
1
|
111.067
|
3.94e-18
|
32.062
|
| HMC_vs_SMC |
2
|
91.514
|
3.31e-17
|
26.418
|
| HMC_vs_SMC |
3
|
127.462
|
8.68e-19
|
36.795
|
| HMC_vs_SMC |
4
|
108.068
|
5.33e-18
|
31.196
|
| Metro_vs_SMC |
0
|
11.416
|
1.94e-07
|
3.296
|
| Metro_vs_SMC |
1
|
110.567
|
4.14e-18
|
31.918
|
| Metro_vs_SMC |
2
|
25.984
|
3.17e-11
|
7.501
|
| Metro_vs_SMC |
3
|
7.941
|
7.01e-06
|
2.292
|
| Metro_vs_SMC |
4
|
14.925
|
1.2e-08
|
4.308
|
| HMC_vs_DEMetro_Z |
0
|
1.642
|
0.129
|
0.474
|
| HMC_vs_DEMetro_Z |
1
|
2.025
|
0.0679
|
0.584
|
| HMC_vs_DEMetro_Z |
2
|
-10.455
|
4.73e-07
|
-3.018
|
| HMC_vs_DEMetro_Z |
3
|
-15.365
|
8.84e-09
|
-4.436
|
| HMC_vs_DEMetro_Z |
4
|
-16.892
|
3.24e-09
|
-4.876
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.619 |
0.014 |
0.007 |
85.157 |
| HMC |
5 |
0.593 |
0.010 |
0.004 |
136.501 |
| HMC |
10 |
0.565 |
0.012 |
0.005 |
119.952 |
| HMC |
15 |
0.537 |
0.012 |
0.004 |
122.506 |
| HMC |
30 |
0.463 |
0.015 |
0.004 |
105.081 |
| SMC |
2 |
0.010 |
0.014 |
0.007 |
-0.481 |
| SMC |
5 |
0.012 |
0.010 |
0.004 |
0.672 |
| SMC |
10 |
0.013 |
0.012 |
0.005 |
0.075 |
| SMC |
15 |
0.013 |
0.012 |
0.004 |
0.094 |
| SMC |
30 |
0.013 |
0.015 |
0.004 |
-0.355 |
| Metro |
2 |
0.566 |
0.014 |
0.007 |
77.725 |
| Metro |
5 |
0.601 |
0.010 |
0.004 |
138.199 |
| Metro |
10 |
0.541 |
0.012 |
0.005 |
114.789 |
| Metro |
15 |
0.436 |
0.012 |
0.004 |
98.956 |
| Metro |
30 |
0.434 |
0.015 |
0.004 |
98.345 |
| DEMetro_Z |
2 |
0.515 |
0.014 |
0.007 |
70.507 |
| DEMetro_Z |
5 |
0.529 |
0.010 |
0.004 |
121.478 |
| DEMetro_Z |
10 |
0.876 |
0.012 |
0.005 |
187.564 |
| DEMetro_Z |
15 |
0.874 |
0.012 |
0.004 |
201.073 |
| DEMetro_Z |
30 |
0.929 |
0.015 |
0.004 |
214.560 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
Mode Transitions
Mode Transitions (scatter)
KDE + Init Plots
Forest & Ridge Plots
Pooled
Chain
Pairwise Scatter Plots
Pooled
Chain
Varying_Mode_Distance_with_high_Dimension
(Mixture,
mm,
12 runs)
Pooled Chains results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
3.335 |
0.0062 |
5.820 |
| HMC |
8 |
7.039 |
2.13e-05 |
53.533 |
| HMC |
10 |
5.548 |
0.000172 |
49.141 |
| HMC |
12 |
4.050 |
0.00191 |
54.186 |
| HMC |
15 |
3.306 |
0.00697 |
26.361 |
| HMC |
18 |
2.413 |
0.0344 |
18.050 |
| SMC |
5 |
0.826 |
0.419 |
0.445 |
| SMC |
8 |
0.924 |
0.366 |
0.442 |
| SMC |
10 |
0.825 |
0.419 |
0.294 |
| SMC |
12 |
2.552 |
0.0188 |
1.218 |
| SMC |
15 |
0.671 |
0.509 |
0.255 |
| SMC |
18 |
-0.618 |
0.543 |
-0.258 |
| Metro |
5 |
6.937 |
1.53e-05 |
9.379 |
| Metro |
8 |
5.178 |
0.000298 |
26.605 |
| Metro |
10 |
5.417 |
0.000206 |
27.500 |
| Metro |
12 |
4.468 |
0.000945 |
44.479 |
| Metro |
15 |
3.385 |
0.00607 |
26.610 |
| Metro |
18 |
2.959 |
0.013 |
21.599 |
| DEMetro_Z |
5 |
22.177 |
1.76e-10 |
2813.387 |
| DEMetro_Z |
8 |
32.172 |
3.11e-12 |
1552.602 |
| DEMetro_Z |
10 |
23.973 |
7.57e-11 |
740.903 |
| DEMetro_Z |
12 |
36.434 |
7.98e-13 |
889.749 |
| DEMetro_Z |
15 |
45.452 |
6.66e-14 |
340.806 |
| DEMetro_Z |
18 |
23.865 |
7.86e-11 |
337.535 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
-22.038
|
1.88e-10
|
-6.362
|
| HMC_vs_DEMetro_Z |
1
|
-32.515
|
2.78e-12
|
-9.386
|
| HMC_vs_DEMetro_Z |
2
|
-25.181
|
4.46e-11
|
-7.269
|
| HMC_vs_DEMetro_Z |
3
|
-31.794
|
3.54e-12
|
-9.178
|
| HMC_vs_DEMetro_Z |
4
|
-26.658
|
2.41e-11
|
-7.695
|
| HMC_vs_DEMetro_Z |
5
|
-19.215
|
8.21e-10
|
-5.547
|
| Metro_vs_SMC |
0
|
6.406
|
5.04e-05
|
1.849
|
| Metro_vs_SMC |
1
|
5.009
|
0.000397
|
1.446
|
| Metro_vs_SMC |
2
|
5.330
|
0.000241
|
1.539
|
| Metro_vs_SMC |
3
|
4.322
|
0.00121
|
1.248
|
| Metro_vs_SMC |
4
|
3.361
|
0.00636
|
0.970
|
| Metro_vs_SMC |
5
|
3.011
|
0.0118
|
0.869
|
| Metro_vs_DEMetro_Z |
0
|
-21.974
|
1.94e-10
|
-6.343
|
| Metro_vs_DEMetro_Z |
1
|
-32.146
|
3.14e-12
|
-9.280
|
| Metro_vs_DEMetro_Z |
2
|
-24.477
|
6.06e-11
|
-7.066
|
| Metro_vs_DEMetro_Z |
3
|
-34.570
|
1.42e-12
|
-9.979
|
| Metro_vs_DEMetro_Z |
4
|
-26.890
|
2.19e-11
|
-7.763
|
| Metro_vs_DEMetro_Z |
5
|
-19.834
|
5.84e-10
|
-5.726
|
| HMC_vs_Metro |
0
|
-1.720
|
0.113
|
-0.496
|
| HMC_vs_Metro |
1
|
3.628
|
0.00397
|
1.047
|
| HMC_vs_Metro |
2
|
2.135
|
0.0561
|
0.616
|
| HMC_vs_Metro |
3
|
1.111
|
0.29
|
0.321
|
| HMC_vs_Metro |
4
|
-1.508
|
0.16
|
-0.435
|
| HMC_vs_Metro |
5
|
-1.150
|
0.275
|
-0.332
|
| HMC_vs_SMC |
0
|
3.553
|
0.00453
|
1.026
|
| HMC_vs_SMC |
1
|
7.077
|
2.05e-05
|
2.043
|
| HMC_vs_SMC |
2
|
5.522
|
0.00018
|
1.594
|
| HMC_vs_SMC |
3
|
3.931
|
0.00235
|
1.135
|
| HMC_vs_SMC |
4
|
3.282
|
0.0073
|
0.948
|
| HMC_vs_SMC |
5
|
2.465
|
0.0314
|
0.711
|
| DEMetro_Z_vs_SMC |
0
|
22.139
|
1.79e-10
|
6.391
|
| DEMetro_Z_vs_SMC |
1
|
32.037
|
3.26e-12
|
9.248
|
| DEMetro_Z_vs_SMC |
2
|
23.958
|
7.64e-11
|
6.916
|
| DEMetro_Z_vs_SMC |
3
|
36.415
|
8.07e-13
|
10.512
|
| DEMetro_Z_vs_SMC |
4
|
44.592
|
8.81e-14
|
12.873
|
| DEMetro_Z_vs_SMC |
5
|
23.905
|
7.83e-11
|
6.901
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
0.036 |
0.023 |
0.002 |
5.820 |
| HMC |
8 |
0.261 |
0.025 |
0.004 |
53.533 |
| HMC |
10 |
0.454 |
0.026 |
0.009 |
49.141 |
| HMC |
12 |
0.414 |
0.030 |
0.007 |
54.186 |
| HMC |
15 |
0.529 |
0.035 |
0.019 |
26.361 |
| HMC |
18 |
0.420 |
0.044 |
0.021 |
18.050 |
| SMC |
5 |
0.024 |
0.023 |
0.002 |
0.445 |
| SMC |
8 |
0.027 |
0.025 |
0.004 |
0.442 |
| SMC |
10 |
0.029 |
0.026 |
0.009 |
0.294 |
| SMC |
12 |
0.038 |
0.030 |
0.007 |
1.218 |
| SMC |
15 |
0.040 |
0.035 |
0.019 |
0.255 |
| SMC |
18 |
0.039 |
0.044 |
0.021 |
-0.258 |
| Metro |
5 |
0.043 |
0.023 |
0.002 |
9.379 |
| Metro |
8 |
0.142 |
0.025 |
0.004 |
26.605 |
| Metro |
10 |
0.266 |
0.026 |
0.009 |
27.500 |
| Metro |
12 |
0.345 |
0.030 |
0.007 |
44.479 |
| Metro |
15 |
0.534 |
0.035 |
0.019 |
26.610 |
| Metro |
18 |
0.494 |
0.044 |
0.021 |
21.599 |
| DEMetro_Z |
5 |
6.211 |
0.023 |
0.002 |
2813.387 |
| DEMetro_Z |
8 |
6.864 |
0.025 |
0.004 |
1552.602 |
| DEMetro_Z |
10 |
6.475 |
0.026 |
0.009 |
740.903 |
| DEMetro_Z |
12 |
6.338 |
0.030 |
0.007 |
889.749 |
| DEMetro_Z |
15 |
6.427 |
0.035 |
0.019 |
340.806 |
| DEMetro_Z |
18 |
7.076 |
0.044 |
0.021 |
337.535 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
1.619 |
0.121 |
0.569 |
| HMC |
8 |
3.229 |
0.00798 |
20.123 |
| HMC |
10 |
3.487 |
0.00508 |
141.997 |
| HMC |
12 |
2.898 |
0.0145 |
101.070 |
| HMC |
15 |
2.609 |
0.0243 |
145.557 |
| HMC |
18 |
2.009 |
0.0698 |
113.693 |
| SMC |
5 |
1.560 |
0.133 |
0.594 |
| SMC |
8 |
1.231 |
0.233 |
0.441 |
| SMC |
10 |
2.570 |
0.0186 |
1.331 |
| SMC |
12 |
3.103 |
0.00607 |
1.713 |
| SMC |
15 |
2.656 |
0.018 |
1.930 |
| SMC |
18 |
2.142 |
0.0467 |
1.266 |
| Metro |
5 |
4.691 |
0.000112 |
1.908 |
| Metro |
8 |
2.611 |
0.0236 |
5.467 |
| Metro |
10 |
3.608 |
0.00411 |
48.276 |
| Metro |
12 |
4.148 |
0.00162 |
66.358 |
| Metro |
15 |
2.646 |
0.0228 |
146.873 |
| Metro |
18 |
2.290 |
0.0428 |
127.253 |
| DEMetro_Z |
5 |
15.719 |
6.95e-09 |
15593.646 |
| DEMetro_Z |
8 |
21.441 |
2.53e-10 |
8248.656 |
| DEMetro_Z |
10 |
27.056 |
2.05e-11 |
17586.087 |
| DEMetro_Z |
12 |
20.717 |
3.66e-10 |
12096.115 |
| DEMetro_Z |
15 |
26.889 |
2.19e-11 |
9396.415 |
| DEMetro_Z |
18 |
24.992 |
4.84e-11 |
7794.524 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
-0.075
|
0.942
|
-0.022
|
| HMC_vs_SMC |
1
|
3.159
|
0.0091
|
0.912
|
| HMC_vs_SMC |
2
|
3.457
|
0.00536
|
0.998
|
| HMC_vs_SMC |
3
|
2.862
|
0.0155
|
0.826
|
| HMC_vs_SMC |
4
|
2.575
|
0.0258
|
0.743
|
| HMC_vs_SMC |
5
|
1.988
|
0.0722
|
0.574
|
| Metro_vs_DEMetro_Z |
0
|
-15.717
|
6.97e-09
|
-4.537
|
| Metro_vs_DEMetro_Z |
1
|
-21.453
|
2.52e-10
|
-6.193
|
| Metro_vs_DEMetro_Z |
2
|
-26.903
|
2.18e-11
|
-7.766
|
| Metro_vs_DEMetro_Z |
3
|
-20.274
|
4.62e-10
|
-5.853
|
| Metro_vs_DEMetro_Z |
4
|
-24.977
|
4.87e-11
|
-7.210
|
| Metro_vs_DEMetro_Z |
5
|
-25.421
|
4.03e-11
|
-7.338
|
| HMC_vs_Metro |
0
|
-4.856
|
0.000506
|
-1.402
|
| HMC_vs_Metro |
1
|
2.451
|
0.0322
|
0.707
|
| HMC_vs_Metro |
2
|
2.165
|
0.0533
|
0.625
|
| HMC_vs_Metro |
3
|
1.216
|
0.249
|
0.351
|
| HMC_vs_Metro |
4
|
-1.845
|
0.0921
|
-0.533
|
| HMC_vs_Metro |
5
|
-0.960
|
0.358
|
-0.277
|
| HMC_vs_DEMetro_Z |
0
|
-15.717
|
6.97e-09
|
-4.537
|
| HMC_vs_DEMetro_Z |
1
|
-21.415
|
2.56e-10
|
-6.182
|
| HMC_vs_DEMetro_Z |
2
|
-26.254
|
2.84e-11
|
-7.579
|
| HMC_vs_DEMetro_Z |
3
|
-20.229
|
4.73e-10
|
-5.840
|
| HMC_vs_DEMetro_Z |
4
|
-24.984
|
4.86e-11
|
-7.212
|
| HMC_vs_DEMetro_Z |
5
|
-25.305
|
4.23e-11
|
-7.305
|
| Metro_vs_SMC |
0
|
3.922
|
0.00238
|
1.132
|
| Metro_vs_SMC |
1
|
2.513
|
0.0289
|
0.725
|
| Metro_vs_SMC |
2
|
3.545
|
0.00459
|
1.023
|
| Metro_vs_SMC |
3
|
4.053
|
0.00191
|
1.170
|
| Metro_vs_SMC |
4
|
2.612
|
0.0242
|
0.754
|
| Metro_vs_SMC |
5
|
2.270
|
0.0443
|
0.655
|
| DEMetro_Z_vs_SMC |
0
|
15.719
|
6.96e-09
|
4.538
|
| DEMetro_Z_vs_SMC |
1
|
21.443
|
2.53e-10
|
6.190
|
| DEMetro_Z_vs_SMC |
2
|
27.050
|
2.05e-11
|
7.809
|
| DEMetro_Z_vs_SMC |
3
|
20.715
|
3.67e-10
|
5.980
|
| DEMetro_Z_vs_SMC |
4
|
26.895
|
2.18e-11
|
7.764
|
| DEMetro_Z_vs_SMC |
5
|
24.991
|
4.84e-11
|
7.214
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
0.047 |
0.041 |
0.011 |
0.569 |
| HMC |
8 |
0.446 |
0.046 |
0.020 |
20.123 |
| HMC |
10 |
1.511 |
0.040 |
0.010 |
141.997 |
| HMC |
12 |
1.529 |
0.045 |
0.015 |
101.070 |
| HMC |
15 |
2.827 |
0.044 |
0.019 |
145.557 |
| HMC |
18 |
2.516 |
0.053 |
0.022 |
113.693 |
| SMC |
5 |
0.047 |
0.041 |
0.011 |
0.594 |
| SMC |
8 |
0.055 |
0.046 |
0.020 |
0.441 |
| SMC |
10 |
0.053 |
0.040 |
0.010 |
1.331 |
| SMC |
12 |
0.070 |
0.045 |
0.015 |
1.713 |
| SMC |
15 |
0.081 |
0.044 |
0.019 |
1.930 |
| SMC |
18 |
0.080 |
0.053 |
0.022 |
1.266 |
| Metro |
5 |
0.062 |
0.041 |
0.011 |
1.908 |
| Metro |
8 |
0.155 |
0.046 |
0.020 |
5.467 |
| Metro |
10 |
0.540 |
0.040 |
0.010 |
48.276 |
| Metro |
12 |
1.019 |
0.045 |
0.015 |
66.358 |
| Metro |
15 |
2.852 |
0.044 |
0.019 |
146.873 |
| Metro |
18 |
2.810 |
0.053 |
0.022 |
127.253 |
| DEMetro_Z |
5 |
172.242 |
0.041 |
0.011 |
15593.646 |
| DEMetro_Z |
8 |
163.985 |
0.046 |
0.020 |
8248.656 |
| DEMetro_Z |
10 |
182.308 |
0.040 |
0.010 |
17586.087 |
| DEMetro_Z |
12 |
177.630 |
0.045 |
0.015 |
12096.115 |
| DEMetro_Z |
15 |
179.662 |
0.044 |
0.019 |
9396.415 |
| DEMetro_Z |
18 |
168.934 |
0.053 |
0.022 |
7794.524 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
3.656 |
0.00353 |
7.212 |
| HMC |
8 |
6.720 |
3.26e-05 |
66.937 |
| HMC |
10 |
5.376 |
0.000224 |
58.728 |
| HMC |
12 |
4.169 |
0.00156 |
78.893 |
| HMC |
15 |
3.315 |
0.00688 |
31.712 |
| HMC |
18 |
2.418 |
0.0341 |
21.035 |
| SMC |
5 |
2.236 |
0.0371 |
1.133 |
| SMC |
8 |
1.240 |
0.229 |
0.560 |
| SMC |
10 |
1.159 |
0.261 |
0.405 |
| SMC |
12 |
3.412 |
0.00301 |
1.854 |
| SMC |
15 |
1.042 |
0.309 |
0.396 |
| SMC |
18 |
-0.625 |
0.538 |
-0.253 |
| Metro |
5 |
7.813 |
4.88e-06 |
10.997 |
| Metro |
8 |
5.301 |
0.000249 |
34.072 |
| Metro |
10 |
5.148 |
0.000315 |
31.407 |
| Metro |
12 |
4.477 |
0.000934 |
67.048 |
| Metro |
15 |
3.429 |
0.00562 |
33.663 |
| Metro |
18 |
3.005 |
0.0119 |
25.242 |
| DEMetro_Z |
5 |
37.043 |
6.69e-13 |
7269.545 |
| DEMetro_Z |
8 |
48.009 |
3.92e-14 |
3833.302 |
| DEMetro_Z |
10 |
56.170 |
7e-15 |
1765.269 |
| DEMetro_Z |
12 |
46.165 |
6.02e-14 |
2617.362 |
| DEMetro_Z |
15 |
54.333 |
9.93e-15 |
829.364 |
| DEMetro_Z |
18 |
38.576 |
4.25e-13 |
699.696 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
-37.004
|
6.77e-13
|
-10.682
|
| Metro_vs_DEMetro_Z |
1
|
-47.705
|
4.21e-14
|
-13.771
|
| Metro_vs_DEMetro_Z |
2
|
-53.648
|
1.16e-14
|
-15.487
|
| Metro_vs_DEMetro_Z |
3
|
-39.194
|
3.61e-13
|
-11.314
|
| Metro_vs_DEMetro_Z |
4
|
-40.673
|
2.41e-13
|
-11.741
|
| Metro_vs_DEMetro_Z |
5
|
-34.039
|
1.68e-12
|
-9.826
|
| DEMetro_Z_vs_SMC |
0
|
37.060
|
6.66e-13
|
10.698
|
| DEMetro_Z_vs_SMC |
1
|
48.027
|
3.91e-14
|
13.864
|
| DEMetro_Z_vs_SMC |
2
|
56.130
|
7.08e-15
|
16.203
|
| DEMetro_Z_vs_SMC |
3
|
46.044
|
6.2e-14
|
13.292
|
| DEMetro_Z_vs_SMC |
4
|
54.004
|
1.08e-14
|
15.590
|
| DEMetro_Z_vs_SMC |
5
|
38.519
|
4.37e-13
|
11.119
|
| HMC_vs_DEMetro_Z |
0
|
-37.069
|
6.64e-13
|
-10.701
|
| HMC_vs_DEMetro_Z |
1
|
-47.553
|
4.36e-14
|
-13.727
|
| HMC_vs_DEMetro_Z |
2
|
-55.682
|
7.73e-15
|
-16.074
|
| HMC_vs_DEMetro_Z |
3
|
-38.627
|
4.24e-13
|
-11.151
|
| HMC_vs_DEMetro_Z |
4
|
-41.076
|
2.16e-13
|
-11.858
|
| HMC_vs_DEMetro_Z |
5
|
-32.721
|
2.59e-12
|
-9.446
|
| HMC_vs_Metro |
0
|
-1.763
|
0.106
|
-0.509
|
| HMC_vs_Metro |
1
|
3.454
|
0.00539
|
0.997
|
| HMC_vs_Metro |
2
|
2.162
|
0.0535
|
0.624
|
| HMC_vs_Metro |
3
|
1.029
|
0.325
|
0.297
|
| HMC_vs_Metro |
4
|
-2.346
|
0.0388
|
-0.677
|
| HMC_vs_Metro |
5
|
-1.117
|
0.288
|
-0.323
|
| HMC_vs_SMC |
0
|
3.547
|
0.00457
|
1.024
|
| HMC_vs_SMC |
1
|
6.723
|
3.27e-05
|
1.941
|
| HMC_vs_SMC |
2
|
5.343
|
0.000236
|
1.542
|
| HMC_vs_SMC |
3
|
4.052
|
0.00191
|
1.170
|
| HMC_vs_SMC |
4
|
3.280
|
0.00734
|
0.947
|
| HMC_vs_SMC |
5
|
2.463
|
0.0315
|
0.711
|
| Metro_vs_SMC |
0
|
6.781
|
3.03e-05
|
1.957
|
| Metro_vs_SMC |
1
|
5.153
|
0.000317
|
1.488
|
| Metro_vs_SMC |
2
|
5.076
|
0.000357
|
1.465
|
| Metro_vs_SMC |
3
|
4.345
|
0.00117
|
1.254
|
| Metro_vs_SMC |
4
|
3.395
|
0.00598
|
0.980
|
| Metro_vs_SMC |
5
|
3.050
|
0.011
|
0.880
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
0.040 |
0.030 |
0.001 |
7.212 |
| HMC |
8 |
0.208 |
0.033 |
0.003 |
66.937 |
| HMC |
10 |
0.372 |
0.035 |
0.006 |
58.728 |
| HMC |
12 |
0.333 |
0.037 |
0.004 |
78.893 |
| HMC |
15 |
0.422 |
0.041 |
0.012 |
31.712 |
| HMC |
18 |
0.343 |
0.049 |
0.014 |
21.035 |
| SMC |
5 |
0.032 |
0.030 |
0.001 |
1.133 |
| SMC |
8 |
0.034 |
0.033 |
0.003 |
0.560 |
| SMC |
10 |
0.037 |
0.035 |
0.006 |
0.405 |
| SMC |
12 |
0.044 |
0.037 |
0.004 |
1.854 |
| SMC |
15 |
0.046 |
0.041 |
0.012 |
0.396 |
| SMC |
18 |
0.046 |
0.049 |
0.014 |
-0.253 |
| Metro |
5 |
0.045 |
0.030 |
0.001 |
10.997 |
| Metro |
8 |
0.122 |
0.033 |
0.003 |
34.072 |
| Metro |
10 |
0.215 |
0.035 |
0.006 |
31.407 |
| Metro |
12 |
0.289 |
0.037 |
0.004 |
67.048 |
| Metro |
15 |
0.446 |
0.041 |
0.012 |
33.663 |
| Metro |
18 |
0.402 |
0.049 |
0.014 |
25.242 |
| DEMetro_Z |
5 |
10.041 |
0.030 |
0.001 |
7269.545 |
| DEMetro_Z |
8 |
10.062 |
0.033 |
0.003 |
3833.302 |
| DEMetro_Z |
10 |
10.187 |
0.035 |
0.006 |
1765.269 |
| DEMetro_Z |
12 |
9.882 |
0.037 |
0.004 |
2617.362 |
| DEMetro_Z |
15 |
10.005 |
0.041 |
0.012 |
829.364 |
| DEMetro_Z |
18 |
9.813 |
0.049 |
0.014 |
699.696 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
3.741 |
0.00285 |
5.390 |
| HMC |
8 |
6.986 |
2.28e-05 |
52.353 |
| HMC |
10 |
5.571 |
0.000166 |
52.333 |
| HMC |
12 |
3.959 |
0.00224 |
69.856 |
| HMC |
15 |
3.326 |
0.00675 |
33.022 |
| HMC |
18 |
2.450 |
0.0322 |
24.578 |
| SMC |
5 |
1.738 |
0.0969 |
0.800 |
| SMC |
8 |
1.329 |
0.197 |
0.563 |
| SMC |
10 |
0.846 |
0.408 |
0.290 |
| SMC |
12 |
3.256 |
0.00387 |
1.559 |
| SMC |
15 |
0.848 |
0.406 |
0.327 |
| SMC |
18 |
-0.239 |
0.814 |
-0.114 |
| Metro |
5 |
7.730 |
4.11e-06 |
8.769 |
| Metro |
8 |
5.101 |
0.000336 |
25.760 |
| Metro |
10 |
5.408 |
0.00021 |
28.586 |
| Metro |
12 |
4.453 |
0.000972 |
57.681 |
| Metro |
15 |
3.432 |
0.00559 |
32.344 |
| Metro |
18 |
2.960 |
0.013 |
31.160 |
| DEMetro_Z |
5 |
43.295 |
1.18e-13 |
458.419 |
| DEMetro_Z |
8 |
101.041 |
5.38e-18 |
276.960 |
| DEMetro_Z |
10 |
59.555 |
1.96e-15 |
158.534 |
| DEMetro_Z |
12 |
70.536 |
3.93e-16 |
248.677 |
| DEMetro_Z |
15 |
52.918 |
3.51e-15 |
94.827 |
| DEMetro_Z |
18 |
50.152 |
1.03e-14 |
110.695 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
42.916
|
1.34e-13
|
12.389
|
| DEMetro_Z_vs_SMC |
1
|
98.019
|
1.56e-17
|
28.296
|
| DEMetro_Z_vs_SMC |
2
|
60.025
|
3.39e-15
|
17.328
|
| DEMetro_Z_vs_SMC |
3
|
68.966
|
7.4e-16
|
19.909
|
| DEMetro_Z_vs_SMC |
4
|
53.901
|
1.1e-14
|
15.560
|
| DEMetro_Z_vs_SMC |
5
|
48.759
|
3.31e-14
|
14.075
|
| HMC_vs_Metro |
0
|
-1.949
|
0.0772
|
-0.563
|
| HMC_vs_Metro |
1
|
3.430
|
0.00562
|
0.990
|
| HMC_vs_Metro |
2
|
2.196
|
0.0504
|
0.634
|
| HMC_vs_Metro |
3
|
1.068
|
0.308
|
0.308
|
| HMC_vs_Metro |
4
|
0.990
|
0.343
|
0.286
|
| HMC_vs_Metro |
5
|
-1.536
|
0.153
|
-0.443
|
| Metro_vs_DEMetro_Z |
0
|
-40.392
|
2.6e-13
|
-11.660
|
| Metro_vs_DEMetro_Z |
1
|
-53.715
|
1.15e-14
|
-15.506
|
| Metro_vs_DEMetro_Z |
2
|
-25.729
|
3.53e-11
|
-7.427
|
| Metro_vs_DEMetro_Z |
3
|
-15.294
|
9.29e-09
|
-4.415
|
| Metro_vs_DEMetro_Z |
4
|
-6.292
|
5.9e-05
|
-1.816
|
| Metro_vs_DEMetro_Z |
5
|
-8.074
|
5.98e-06
|
-2.331
|
| HMC_vs_SMC |
0
|
3.802
|
0.00293
|
1.098
|
| HMC_vs_SMC |
1
|
7.034
|
2.17e-05
|
2.031
|
| HMC_vs_SMC |
2
|
5.549
|
0.000173
|
1.602
|
| HMC_vs_SMC |
3
|
3.845
|
0.00272
|
1.110
|
| HMC_vs_SMC |
4
|
3.305
|
0.00701
|
0.954
|
| HMC_vs_SMC |
5
|
2.461
|
0.0316
|
0.711
|
| Metro_vs_SMC |
0
|
6.950
|
2.42e-05
|
2.006
|
| Metro_vs_SMC |
1
|
4.950
|
0.000436
|
1.429
|
| Metro_vs_SMC |
2
|
5.339
|
0.000238
|
1.541
|
| Metro_vs_SMC |
3
|
4.295
|
0.00127
|
1.240
|
| Metro_vs_SMC |
4
|
3.411
|
0.00582
|
0.985
|
| Metro_vs_SMC |
5
|
2.963
|
0.0129
|
0.855
|
| HMC_vs_DEMetro_Z |
0
|
-41.858
|
1.76e-13
|
-12.083
|
| HMC_vs_DEMetro_Z |
1
|
-25.010
|
4.8e-11
|
-7.220
|
| HMC_vs_DEMetro_Z |
2
|
-12.037
|
1.13e-07
|
-3.475
|
| HMC_vs_DEMetro_Z |
3
|
-11.053
|
2.69e-07
|
-3.191
|
| HMC_vs_DEMetro_Z |
4
|
-5.942
|
9.7e-05
|
-1.715
|
| HMC_vs_DEMetro_Z |
5
|
-9.290
|
1.54e-06
|
-2.682
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
0.020 |
0.013 |
0.001 |
5.390 |
| HMC |
8 |
0.119 |
0.013 |
0.002 |
52.353 |
| HMC |
10 |
0.196 |
0.013 |
0.004 |
52.333 |
| HMC |
12 |
0.170 |
0.013 |
0.002 |
69.856 |
| HMC |
15 |
0.200 |
0.013 |
0.006 |
33.022 |
| HMC |
18 |
0.137 |
0.014 |
0.005 |
24.578 |
| SMC |
5 |
0.014 |
0.013 |
0.001 |
0.800 |
| SMC |
8 |
0.014 |
0.013 |
0.002 |
0.563 |
| SMC |
10 |
0.014 |
0.013 |
0.004 |
0.290 |
| SMC |
12 |
0.017 |
0.013 |
0.002 |
1.559 |
| SMC |
15 |
0.015 |
0.013 |
0.006 |
0.327 |
| SMC |
18 |
0.014 |
0.014 |
0.005 |
-0.114 |
| Metro |
5 |
0.024 |
0.013 |
0.001 |
8.769 |
| Metro |
8 |
0.065 |
0.013 |
0.002 |
25.760 |
| Metro |
10 |
0.113 |
0.013 |
0.004 |
28.586 |
| Metro |
12 |
0.142 |
0.013 |
0.002 |
57.681 |
| Metro |
15 |
0.197 |
0.013 |
0.006 |
32.344 |
| Metro |
18 |
0.169 |
0.014 |
0.005 |
31.160 |
| DEMetro_Z |
5 |
0.575 |
0.013 |
0.001 |
458.419 |
| DEMetro_Z |
8 |
0.573 |
0.013 |
0.002 |
276.960 |
| DEMetro_Z |
10 |
0.569 |
0.013 |
0.004 |
158.534 |
| DEMetro_Z |
12 |
0.570 |
0.013 |
0.002 |
248.677 |
| DEMetro_Z |
15 |
0.551 |
0.013 |
0.006 |
94.827 |
| DEMetro_Z |
18 |
0.565 |
0.014 |
0.005 |
110.695 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
R Hat (scatter)
Mode Transitions
One Chain results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
3.018 |
0.0112 |
6.106 |
| HMC |
8 |
5.052 |
0.000371 |
96.304 |
| HMC |
10 |
156.994 |
4.58e-27 |
102.091 |
| HMC |
12 |
177.193 |
1.07e-24 |
149.019 |
| HMC |
15 |
159.395 |
1.82e-34 |
70.992 |
| HMC |
18 |
164.808 |
4.85e-34 |
76.613 |
| SMC |
5 |
1.645 |
0.117 |
0.903 |
| SMC |
8 |
1.082 |
0.291 |
0.434 |
| SMC |
10 |
0.972 |
0.342 |
0.437 |
| SMC |
12 |
1.402 |
0.179 |
0.876 |
| SMC |
15 |
0.060 |
0.953 |
0.021 |
| SMC |
18 |
-0.404 |
0.69 |
-0.157 |
| Metro |
5 |
6.594 |
2.66e-05 |
9.541 |
| Metro |
8 |
4.785 |
0.000559 |
28.853 |
| Metro |
10 |
3.346 |
0.00651 |
36.781 |
| Metro |
12 |
29.774 |
6.31e-12 |
144.587 |
| Metro |
15 |
153.298 |
1.88e-33 |
70.997 |
| Metro |
18 |
145.859 |
1.83e-30 |
76.612 |
| DEMetro_Z |
5 |
16.738 |
3.58e-09 |
4689.347 |
| DEMetro_Z |
8 |
14.456 |
1.68e-08 |
2458.663 |
| DEMetro_Z |
10 |
16.136 |
5.27e-09 |
1247.983 |
| DEMetro_Z |
12 |
11.509 |
1.78e-07 |
1391.846 |
| DEMetro_Z |
15 |
16.533 |
4.07e-09 |
544.160 |
| DEMetro_Z |
18 |
18.772 |
1.05e-09 |
482.105 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
-16.760
|
3.53e-09
|
-4.838
|
| HMC_vs_DEMetro_Z |
1
|
-13.835
|
2.66e-08
|
-3.994
|
| HMC_vs_DEMetro_Z |
2
|
-14.784
|
1.33e-08
|
-4.268
|
| HMC_vs_DEMetro_Z |
3
|
-10.276
|
5.63e-07
|
-2.966
|
| HMC_vs_DEMetro_Z |
4
|
-14.373
|
1.79e-08
|
-4.149
|
| HMC_vs_DEMetro_Z |
5
|
-15.746
|
6.83e-09
|
-4.545
|
| Metro_vs_SMC |
0
|
5.083
|
0.000353
|
1.467
|
| Metro_vs_SMC |
1
|
4.635
|
0.000722
|
1.338
|
| Metro_vs_SMC |
2
|
3.318
|
0.00686
|
0.958
|
| Metro_vs_SMC |
3
|
28.371
|
1.22e-11
|
8.190
|
| Metro_vs_SMC |
4
|
165.271
|
4.99e-20
|
47.710
|
| Metro_vs_SMC |
5
|
170.335
|
3.58e-20
|
49.172
|
| Metro_vs_DEMetro_Z |
0
|
-16.721
|
3.61e-09
|
-4.827
|
| Metro_vs_DEMetro_Z |
1
|
-14.258
|
1.94e-08
|
-4.116
|
| Metro_vs_DEMetro_Z |
2
|
-16.049
|
5.58e-09
|
-4.633
|
| Metro_vs_DEMetro_Z |
3
|
-10.273
|
5.64e-07
|
-2.966
|
| Metro_vs_DEMetro_Z |
4
|
-14.380
|
1.78e-08
|
-4.151
|
| Metro_vs_DEMetro_Z |
5
|
-15.733
|
6.89e-09
|
-4.542
|
| HMC_vs_Metro |
0
|
-1.394
|
0.191
|
-0.402
|
| HMC_vs_Metro |
1
|
3.421
|
0.00572
|
0.987
|
| HMC_vs_Metro |
2
|
5.847
|
0.000111
|
1.688
|
| HMC_vs_Metro |
3
|
0.973
|
0.352
|
0.281
|
| HMC_vs_Metro |
4
|
-0.057
|
0.955
|
-0.016
|
| HMC_vs_Metro |
5
|
0.005
|
0.996
|
0.002
|
| HMC_vs_SMC |
0
|
2.792
|
0.0175
|
0.806
|
| HMC_vs_SMC |
1
|
5.020
|
0.00039
|
1.449
|
| HMC_vs_SMC |
2
|
126.356
|
9.55e-19
|
36.476
|
| HMC_vs_SMC |
3
|
134.410
|
4.84e-19
|
38.801
|
| HMC_vs_SMC |
4
|
167.151
|
4.41e-20
|
48.252
|
| HMC_vs_SMC |
5
|
217.073
|
2.49e-21
|
62.663
|
| DEMetro_Z_vs_SMC |
0
|
16.742
|
3.57e-09
|
4.833
|
| DEMetro_Z_vs_SMC |
1
|
14.468
|
1.67e-08
|
4.177
|
| DEMetro_Z_vs_SMC |
2
|
16.149
|
5.23e-09
|
4.662
|
| DEMetro_Z_vs_SMC |
3
|
11.494
|
1.81e-07
|
3.318
|
| DEMetro_Z_vs_SMC |
4
|
16.518
|
4.12e-09
|
4.768
|
| DEMetro_Z_vs_SMC |
5
|
18.834
|
1.02e-09
|
5.437
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
0.036 |
0.023 |
0.002 |
6.106 |
| HMC |
8 |
0.449 |
0.025 |
0.004 |
96.304 |
| HMC |
10 |
0.915 |
0.026 |
0.009 |
102.091 |
| HMC |
12 |
1.086 |
0.030 |
0.007 |
149.019 |
| HMC |
15 |
1.367 |
0.035 |
0.019 |
70.992 |
| HMC |
18 |
1.640 |
0.044 |
0.021 |
76.613 |
| SMC |
5 |
0.025 |
0.023 |
0.002 |
0.903 |
| SMC |
8 |
0.027 |
0.025 |
0.004 |
0.434 |
| SMC |
10 |
0.030 |
0.026 |
0.009 |
0.437 |
| SMC |
12 |
0.036 |
0.030 |
0.007 |
0.876 |
| SMC |
15 |
0.035 |
0.035 |
0.019 |
0.021 |
| SMC |
18 |
0.041 |
0.044 |
0.021 |
-0.157 |
| Metro |
5 |
0.044 |
0.023 |
0.002 |
9.541 |
| Metro |
8 |
0.152 |
0.025 |
0.004 |
28.853 |
| Metro |
10 |
0.347 |
0.026 |
0.009 |
36.781 |
| Metro |
12 |
1.055 |
0.030 |
0.007 |
144.587 |
| Metro |
15 |
1.367 |
0.035 |
0.019 |
70.997 |
| Metro |
18 |
1.640 |
0.044 |
0.021 |
76.612 |
| DEMetro_Z |
5 |
10.338 |
0.023 |
0.002 |
4689.347 |
| DEMetro_Z |
8 |
10.856 |
0.025 |
0.004 |
2458.663 |
| DEMetro_Z |
10 |
10.889 |
0.026 |
0.009 |
1247.983 |
| DEMetro_Z |
12 |
9.898 |
0.030 |
0.007 |
1391.846 |
| DEMetro_Z |
15 |
10.242 |
0.035 |
0.019 |
544.160 |
| DEMetro_Z |
18 |
10.087 |
0.044 |
0.021 |
482.105 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
1.306 |
0.205 |
0.577 |
| HMC |
8 |
3.876 |
0.00258 |
73.272 |
| HMC |
10 |
496.000 |
2.02e-30 |
434.778 |
| HMC |
12 |
758.922 |
9.27e-41 |
444.734 |
| HMC |
15 |
821.429 |
1.47e-38 |
535.737 |
| HMC |
18 |
889.173 |
7.07e-36 |
680.021 |
| SMC |
5 |
-1.360 |
0.194 |
-0.425 |
| SMC |
8 |
-0.950 |
0.354 |
-0.323 |
| SMC |
10 |
1.336 |
0.2 |
0.851 |
| SMC |
12 |
1.640 |
0.121 |
1.075 |
| SMC |
15 |
2.702 |
0.0138 |
1.351 |
| SMC |
18 |
1.936 |
0.0679 |
1.023 |
| Metro |
5 |
3.685 |
0.00146 |
1.807 |
| Metro |
8 |
2.551 |
0.0266 |
7.249 |
| Metro |
10 |
2.542 |
0.0274 |
118.851 |
| Metro |
12 |
17.470 |
2.26e-09 |
420.862 |
| Metro |
15 |
860.668 |
4.9e-40 |
535.971 |
| Metro |
18 |
934.426 |
4.37e-37 |
680.212 |
| DEMetro_Z |
5 |
7.531 |
1.16e-05 |
1994.308 |
| DEMetro_Z |
8 |
8.553 |
3.44e-06 |
1016.153 |
| DEMetro_Z |
10 |
12.738 |
6.28e-08 |
1883.917 |
| DEMetro_Z |
12 |
17.992 |
1.66e-09 |
1437.774 |
| DEMetro_Z |
15 |
12.513 |
7.56e-08 |
1136.426 |
| DEMetro_Z |
18 |
12.827 |
5.84e-08 |
1173.729 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
3.054
|
0.011
|
0.882
|
| HMC_vs_SMC |
1
|
3.899
|
0.00248
|
1.126
|
| HMC_vs_SMC |
2
|
335.614
|
2.06e-23
|
96.883
|
| HMC_vs_SMC |
3
|
1257.572
|
1.01e-29
|
363.030
|
| HMC_vs_SMC |
4
|
1129.955
|
3.28e-29
|
326.190
|
| HMC_vs_SMC |
5
|
853.099
|
7.21e-28
|
246.269
|
| Metro_vs_DEMetro_Z |
0
|
-7.521
|
1.17e-05
|
-2.171
|
| Metro_vs_DEMetro_Z |
1
|
-8.462
|
3.81e-06
|
-2.443
|
| Metro_vs_DEMetro_Z |
2
|
-14.010
|
2.33e-08
|
-4.044
|
| Metro_vs_DEMetro_Z |
3
|
-12.626
|
6.89e-08
|
-3.645
|
| Metro_vs_DEMetro_Z |
4
|
-6.628
|
3.72e-05
|
-1.913
|
| Metro_vs_DEMetro_Z |
5
|
-5.377
|
0.000224
|
-1.552
|
| HMC_vs_Metro |
0
|
-3.781
|
0.00304
|
-1.091
|
| HMC_vs_Metro |
1
|
3.523
|
0.00477
|
1.017
|
| HMC_vs_Metro |
2
|
6.791
|
2.99e-05
|
1.960
|
| HMC_vs_Metro |
3
|
0.990
|
0.344
|
0.286
|
| HMC_vs_Metro |
4
|
-1.582
|
0.142
|
-0.457
|
| HMC_vs_Metro |
5
|
-1.912
|
0.0822
|
-0.552
|
| HMC_vs_DEMetro_Z |
0
|
-7.527
|
1.16e-05
|
-2.173
|
| HMC_vs_DEMetro_Z |
1
|
-7.699
|
9.39e-06
|
-2.222
|
| HMC_vs_DEMetro_Z |
2
|
-9.822
|
8.84e-07
|
-2.835
|
| HMC_vs_DEMetro_Z |
3
|
-12.378
|
8.45e-08
|
-3.573
|
| HMC_vs_DEMetro_Z |
4
|
-6.630
|
3.71e-05
|
-1.914
|
| HMC_vs_DEMetro_Z |
5
|
-5.375
|
0.000225
|
-1.552
|
| Metro_vs_SMC |
0
|
6.128
|
7.44e-05
|
1.769
|
| Metro_vs_SMC |
1
|
2.616
|
0.024
|
0.755
|
| Metro_vs_SMC |
2
|
2.522
|
0.0284
|
0.728
|
| Metro_vs_SMC |
3
|
17.321
|
2.49e-09
|
5.000
|
| Metro_vs_SMC |
4
|
1193.027
|
1.8e-29
|
344.397
|
| Metro_vs_SMC |
5
|
891.520
|
4.44e-28
|
257.360
|
| DEMetro_Z_vs_SMC |
0
|
7.533
|
1.15e-05
|
2.175
|
| DEMetro_Z_vs_SMC |
1
|
8.562
|
3.41e-06
|
2.472
|
| DEMetro_Z_vs_SMC |
2
|
12.730
|
6.33e-08
|
3.675
|
| DEMetro_Z_vs_SMC |
3
|
17.931
|
1.72e-09
|
5.176
|
| DEMetro_Z_vs_SMC |
4
|
12.523
|
7.49e-08
|
3.615
|
| DEMetro_Z_vs_SMC |
5
|
12.829
|
5.84e-08
|
3.704
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
0.047 |
0.041 |
0.011 |
0.577 |
| HMC |
8 |
1.503 |
0.046 |
0.020 |
73.272 |
| HMC |
10 |
4.546 |
0.040 |
0.010 |
434.778 |
| HMC |
12 |
6.574 |
0.045 |
0.015 |
444.734 |
| HMC |
15 |
10.285 |
0.044 |
0.019 |
535.737 |
| HMC |
18 |
14.787 |
0.053 |
0.022 |
680.021 |
| SMC |
5 |
0.036 |
0.041 |
0.011 |
-0.425 |
| SMC |
8 |
0.040 |
0.046 |
0.020 |
-0.323 |
| SMC |
10 |
0.048 |
0.040 |
0.010 |
0.851 |
| SMC |
12 |
0.061 |
0.045 |
0.015 |
1.075 |
| SMC |
15 |
0.070 |
0.044 |
0.019 |
1.351 |
| SMC |
18 |
0.075 |
0.053 |
0.022 |
1.023 |
| Metro |
5 |
0.061 |
0.041 |
0.011 |
1.807 |
| Metro |
8 |
0.190 |
0.046 |
0.020 |
7.249 |
| Metro |
10 |
1.271 |
0.040 |
0.010 |
118.851 |
| Metro |
12 |
6.224 |
0.045 |
0.015 |
420.862 |
| Metro |
15 |
10.290 |
0.044 |
0.019 |
535.971 |
| Metro |
18 |
14.791 |
0.053 |
0.022 |
680.212 |
| DEMetro_Z |
5 |
22.064 |
0.041 |
0.011 |
1994.308 |
| DEMetro_Z |
8 |
20.242 |
0.046 |
0.020 |
1016.153 |
| DEMetro_Z |
10 |
19.565 |
0.040 |
0.010 |
1883.917 |
| DEMetro_Z |
12 |
21.153 |
0.045 |
0.015 |
1437.774 |
| DEMetro_Z |
15 |
21.768 |
0.044 |
0.019 |
1136.426 |
| DEMetro_Z |
18 |
25.484 |
0.053 |
0.022 |
1173.729 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
3.307 |
0.0067 |
7.519 |
| HMC |
8 |
5.028 |
0.000385 |
126.336 |
| HMC |
10 |
115.711 |
7.45e-21 |
117.858 |
| HMC |
12 |
74.567 |
1.78e-16 |
219.087 |
| HMC |
15 |
74.426 |
9.23e-18 |
89.151 |
| HMC |
18 |
79.088 |
2.73e-18 |
89.386 |
| SMC |
5 |
1.917 |
0.072 |
1.137 |
| SMC |
8 |
0.798 |
0.434 |
0.336 |
| SMC |
10 |
0.956 |
0.35 |
0.420 |
| SMC |
12 |
1.844 |
0.0847 |
1.310 |
| SMC |
15 |
0.382 |
0.707 |
0.132 |
| SMC |
18 |
-0.379 |
0.708 |
-0.153 |
| Metro |
5 |
7.275 |
1.09e-05 |
11.301 |
| Metro |
8 |
4.768 |
0.000578 |
37.211 |
| Metro |
10 |
3.245 |
0.00779 |
43.274 |
| Metro |
12 |
27.694 |
1.51e-11 |
214.335 |
| Metro |
15 |
57.996 |
6.89e-16 |
87.983 |
| Metro |
18 |
67.931 |
6.12e-17 |
91.940 |
| DEMetro_Z |
5 |
17.152 |
2.76e-09 |
6258.291 |
| DEMetro_Z |
8 |
15.277 |
9.4e-09 |
3464.455 |
| DEMetro_Z |
10 |
17.555 |
2.15e-09 |
1574.680 |
| DEMetro_Z |
12 |
12.336 |
8.75e-08 |
2162.534 |
| DEMetro_Z |
15 |
16.529 |
4.08e-09 |
702.536 |
| DEMetro_Z |
18 |
19.492 |
7.02e-10 |
612.086 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
-17.141
|
2.78e-09
|
-4.948
|
| Metro_vs_DEMetro_Z |
1
|
-15.107
|
1.06e-08
|
-4.361
|
| Metro_vs_DEMetro_Z |
2
|
-17.465
|
2.28e-09
|
-5.042
|
| Metro_vs_DEMetro_Z |
3
|
-11.215
|
2.32e-07
|
-3.238
|
| Metro_vs_DEMetro_Z |
4
|
-14.455
|
1.68e-08
|
-4.173
|
| Metro_vs_DEMetro_Z |
5
|
-16.488
|
4.19e-09
|
-4.760
|
| DEMetro_Z_vs_SMC |
0
|
17.149
|
2.76e-09
|
4.950
|
| DEMetro_Z_vs_SMC |
1
|
15.287
|
9.33e-09
|
4.413
|
| DEMetro_Z_vs_SMC |
2
|
17.567
|
2.14e-09
|
5.071
|
| DEMetro_Z_vs_SMC |
3
|
12.323
|
8.85e-08
|
3.557
|
| DEMetro_Z_vs_SMC |
4
|
16.520
|
4.11e-09
|
4.769
|
| DEMetro_Z_vs_SMC |
5
|
19.528
|
6.9e-10
|
5.637
|
| HMC_vs_DEMetro_Z |
0
|
-17.161
|
2.74e-09
|
-4.954
|
| HMC_vs_DEMetro_Z |
1
|
-14.561
|
1.56e-08
|
-4.203
|
| HMC_vs_DEMetro_Z |
2
|
-16.282
|
4.79e-09
|
-4.700
|
| HMC_vs_DEMetro_Z |
3
|
-11.074
|
2.64e-07
|
-3.197
|
| HMC_vs_DEMetro_Z |
4
|
-14.640
|
1.47e-08
|
-4.226
|
| HMC_vs_DEMetro_Z |
5
|
-16.850
|
3.33e-09
|
-4.864
|
| HMC_vs_Metro |
0
|
-1.424
|
0.182
|
-0.411
|
| HMC_vs_Metro |
1
|
3.365
|
0.0063
|
0.971
|
| HMC_vs_Metro |
2
|
5.781
|
0.000123
|
1.669
|
| HMC_vs_Metro |
3
|
0.623
|
0.546
|
0.180
|
| HMC_vs_Metro |
4
|
0.751
|
0.469
|
0.217
|
| HMC_vs_Metro |
5
|
-1.360
|
0.201
|
-0.393
|
| HMC_vs_SMC |
0
|
3.122
|
0.00972
|
0.901
|
| HMC_vs_SMC |
1
|
5.009
|
0.000397
|
1.446
|
| HMC_vs_SMC |
2
|
128.727
|
7.78e-19
|
37.160
|
| HMC_vs_SMC |
3
|
69.183
|
7.14e-16
|
19.971
|
| HMC_vs_SMC |
4
|
73.190
|
3.85e-16
|
21.128
|
| HMC_vs_SMC |
5
|
83.600
|
8.94e-17
|
24.133
|
| Metro_vs_SMC |
0
|
5.675
|
0.000143
|
1.638
|
| Metro_vs_SMC |
1
|
4.672
|
0.000681
|
1.349
|
| Metro_vs_SMC |
2
|
3.219
|
0.00817
|
0.929
|
| Metro_vs_SMC |
3
|
26.409
|
2.66e-11
|
7.624
|
| Metro_vs_SMC |
4
|
57.478
|
5.46e-15
|
16.592
|
| Metro_vs_SMC |
5
|
70.346
|
5.95e-16
|
20.307
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
0.040 |
0.030 |
0.001 |
7.519 |
| HMC |
8 |
0.363 |
0.033 |
0.003 |
126.336 |
| HMC |
10 |
0.712 |
0.035 |
0.006 |
117.858 |
| HMC |
12 |
0.861 |
0.037 |
0.004 |
219.087 |
| HMC |
15 |
1.112 |
0.041 |
0.012 |
89.151 |
| HMC |
18 |
1.297 |
0.049 |
0.014 |
89.386 |
| SMC |
5 |
0.032 |
0.030 |
0.001 |
1.137 |
| SMC |
8 |
0.034 |
0.033 |
0.003 |
0.336 |
| SMC |
10 |
0.037 |
0.035 |
0.006 |
0.420 |
| SMC |
12 |
0.042 |
0.037 |
0.004 |
1.310 |
| SMC |
15 |
0.043 |
0.041 |
0.012 |
0.132 |
| SMC |
18 |
0.047 |
0.049 |
0.014 |
-0.153 |
| Metro |
5 |
0.046 |
0.030 |
0.001 |
11.301 |
| Metro |
8 |
0.130 |
0.033 |
0.003 |
37.211 |
| Metro |
10 |
0.284 |
0.035 |
0.006 |
43.274 |
| Metro |
12 |
0.843 |
0.037 |
0.004 |
214.335 |
| Metro |
15 |
1.098 |
0.041 |
0.012 |
87.983 |
| Metro |
18 |
1.332 |
0.049 |
0.014 |
91.940 |
| DEMetro_Z |
5 |
8.649 |
0.030 |
0.001 |
6258.291 |
| DEMetro_Z |
8 |
9.097 |
0.033 |
0.003 |
3464.455 |
| DEMetro_Z |
10 |
9.091 |
0.035 |
0.006 |
1574.680 |
| DEMetro_Z |
12 |
8.172 |
0.037 |
0.004 |
2162.534 |
| DEMetro_Z |
15 |
8.482 |
0.041 |
0.012 |
702.536 |
| DEMetro_Z |
18 |
8.591 |
0.049 |
0.014 |
612.086 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
3.160 |
0.0085 |
5.374 |
| HMC |
8 |
4.988 |
0.00041 |
94.721 |
| HMC |
10 |
77.536 |
1.76e-17 |
111.862 |
| HMC |
12 |
103.290 |
1.86e-18 |
195.891 |
| HMC |
15 |
80.016 |
1.78e-18 |
87.575 |
| HMC |
18 |
103.445 |
3.08e-20 |
105.146 |
| SMC |
5 |
1.838 |
0.0797 |
0.790 |
| SMC |
8 |
1.240 |
0.229 |
0.457 |
| SMC |
10 |
0.818 |
0.422 |
0.360 |
| SMC |
12 |
1.567 |
0.137 |
1.053 |
| SMC |
15 |
0.249 |
0.806 |
0.083 |
| SMC |
18 |
-0.094 |
0.926 |
-0.045 |
| Metro |
5 |
6.803 |
1.78e-05 |
8.798 |
| Metro |
8 |
4.959 |
0.000423 |
27.114 |
| Metro |
10 |
3.310 |
0.00695 |
39.689 |
| Metro |
12 |
26.983 |
1.98e-11 |
186.618 |
| Metro |
15 |
128.146 |
5.04e-25 |
87.127 |
| Metro |
18 |
105.386 |
1.83e-20 |
104.706 |
| DEMetro_Z |
5 |
40.349 |
2.6e-13 |
739.455 |
| DEMetro_Z |
8 |
35.474 |
1.05e-12 |
468.053 |
| DEMetro_Z |
10 |
59.012 |
3.26e-15 |
261.211 |
| DEMetro_Z |
12 |
56.797 |
5.71e-15 |
403.975 |
| DEMetro_Z |
15 |
61.521 |
1.31e-15 |
159.035 |
| DEMetro_Z |
18 |
53.584 |
8.02e-15 |
179.068 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
40.653
|
2.42e-13
|
11.735
|
| DEMetro_Z_vs_SMC |
1
|
35.802
|
9.71e-13
|
10.335
|
| DEMetro_Z_vs_SMC |
2
|
59.367
|
3.83e-15
|
17.138
|
| DEMetro_Z_vs_SMC |
3
|
57.639
|
5.29e-15
|
16.639
|
| DEMetro_Z_vs_SMC |
4
|
60.243
|
3.26e-15
|
17.391
|
| DEMetro_Z_vs_SMC |
5
|
54.313
|
1.02e-14
|
15.679
|
| HMC_vs_Metro |
0
|
-1.675
|
0.122
|
-0.484
|
| HMC_vs_Metro |
1
|
3.530
|
0.00472
|
1.019
|
| HMC_vs_Metro |
2
|
5.738
|
0.000131
|
1.656
|
| HMC_vs_Metro |
3
|
1.337
|
0.208
|
0.386
|
| HMC_vs_Metro |
4
|
0.453
|
0.66
|
0.131
|
| HMC_vs_Metro |
5
|
0.406
|
0.692
|
0.117
|
| Metro_vs_DEMetro_Z |
0
|
-38.981
|
3.84e-13
|
-11.253
|
| Metro_vs_DEMetro_Z |
1
|
-31.771
|
3.57e-12
|
-9.172
|
| Metro_vs_DEMetro_Z |
2
|
-15.596
|
7.56e-09
|
-4.502
|
| Metro_vs_DEMetro_Z |
3
|
-21.917
|
2e-10
|
-6.327
|
| Metro_vs_DEMetro_Z |
4
|
-28.127
|
1.34e-11
|
-8.120
|
| Metro_vs_DEMetro_Z |
5
|
-21.523
|
2.43e-10
|
-6.213
|
| HMC_vs_SMC |
0
|
2.866
|
0.0153
|
0.827
|
| HMC_vs_SMC |
1
|
4.948
|
0.000437
|
1.428
|
| HMC_vs_SMC |
2
|
69.873
|
6.41e-16
|
20.171
|
| HMC_vs_SMC |
3
|
83.413
|
9.16e-17
|
24.079
|
| HMC_vs_SMC |
4
|
78.852
|
1.7e-16
|
22.762
|
| HMC_vs_SMC |
5
|
118.318
|
1.97e-18
|
34.156
|
| Metro_vs_SMC |
0
|
5.633
|
0.000153
|
1.626
|
| Metro_vs_SMC |
1
|
4.816
|
0.000539
|
1.390
|
| Metro_vs_SMC |
2
|
3.281
|
0.00732
|
0.947
|
| Metro_vs_SMC |
3
|
25.906
|
3.28e-11
|
7.478
|
| Metro_vs_SMC |
4
|
135.435
|
4.45e-19
|
39.097
|
| Metro_vs_SMC |
5
|
126.859
|
9.14e-19
|
36.621
|
| HMC_vs_DEMetro_Z |
0
|
-42.391
|
1.53e-13
|
-12.237
|
| HMC_vs_DEMetro_Z |
1
|
-16.774
|
3.5e-09
|
-4.842
|
| HMC_vs_DEMetro_Z |
2
|
-31.362
|
4.11e-12
|
-9.054
|
| HMC_vs_DEMetro_Z |
3
|
-27.009
|
2.09e-11
|
-7.797
|
| HMC_vs_DEMetro_Z |
4
|
-32.383
|
2.9e-12
|
-9.348
|
| HMC_vs_DEMetro_Z |
5
|
-20.472
|
4.16e-10
|
-5.910
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
0.020 |
0.013 |
0.001 |
5.374 |
| HMC |
8 |
0.204 |
0.013 |
0.002 |
94.721 |
| HMC |
10 |
0.405 |
0.013 |
0.004 |
111.862 |
| HMC |
12 |
0.452 |
0.013 |
0.002 |
195.891 |
| HMC |
15 |
0.510 |
0.013 |
0.006 |
87.575 |
| HMC |
18 |
0.537 |
0.014 |
0.005 |
105.146 |
| SMC |
5 |
0.014 |
0.013 |
0.001 |
0.790 |
| SMC |
8 |
0.014 |
0.013 |
0.002 |
0.457 |
| SMC |
10 |
0.014 |
0.013 |
0.004 |
0.360 |
| SMC |
12 |
0.016 |
0.013 |
0.002 |
1.053 |
| SMC |
15 |
0.013 |
0.013 |
0.006 |
0.083 |
| SMC |
18 |
0.014 |
0.014 |
0.005 |
-0.045 |
| Metro |
5 |
0.024 |
0.013 |
0.001 |
8.798 |
| Metro |
8 |
0.068 |
0.013 |
0.002 |
27.114 |
| Metro |
10 |
0.152 |
0.013 |
0.004 |
39.689 |
| Metro |
12 |
0.431 |
0.013 |
0.002 |
186.618 |
| Metro |
15 |
0.508 |
0.013 |
0.006 |
87.127 |
| Metro |
18 |
0.535 |
0.014 |
0.005 |
104.706 |
| DEMetro_Z |
5 |
0.919 |
0.013 |
0.001 |
739.455 |
| DEMetro_Z |
8 |
0.958 |
0.013 |
0.002 |
468.053 |
| DEMetro_Z |
10 |
0.929 |
0.013 |
0.004 |
261.211 |
| DEMetro_Z |
12 |
0.918 |
0.013 |
0.002 |
403.975 |
| DEMetro_Z |
15 |
0.916 |
0.013 |
0.006 |
159.035 |
| DEMetro_Z |
18 |
0.905 |
0.014 |
0.005 |
179.068 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
Mode Transitions
Mode Transitions (scatter)
Forest & Ridge Plots
Pooled
Chain
Pairwise Scatter Plots
Pooled
Chain
Varying_Mode_Distance_with_high_Correlation
(Mixture,
mm,
12 runs)
Pooled Chains results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
2.966 |
0.0128 |
27.607 |
| HMC |
8 |
7.968 |
6.51e-06 |
40.163 |
| HMC |
10 |
3.947 |
0.00227 |
33.381 |
| HMC |
12 |
5.472 |
0.000192 |
42.519 |
| HMC |
15 |
3.945 |
0.00229 |
47.699 |
| HMC |
18 |
3.991 |
0.00207 |
14.533 |
| SMC |
5 |
0.460 |
0.65 |
0.206 |
| SMC |
8 |
0.150 |
0.882 |
0.078 |
| SMC |
10 |
2.146 |
0.0435 |
0.960 |
| SMC |
12 |
0.048 |
0.962 |
0.018 |
| SMC |
15 |
0.007 |
0.994 |
0.003 |
| SMC |
18 |
0.148 |
0.884 |
0.054 |
| Metro |
5 |
5.772 |
0.000123 |
48.150 |
| Metro |
8 |
5.591 |
0.000161 |
43.416 |
| Metro |
10 |
3.515 |
0.00484 |
44.409 |
| Metro |
12 |
4.947 |
0.000434 |
36.972 |
| Metro |
15 |
4.947 |
0.000435 |
48.246 |
| Metro |
18 |
3.925 |
0.00232 |
14.134 |
| DEMetro_Z |
5 |
3.694 |
0.00353 |
34.497 |
| DEMetro_Z |
8 |
4.514 |
0.000871 |
28.034 |
| DEMetro_Z |
10 |
3.521 |
0.00478 |
52.959 |
| DEMetro_Z |
12 |
5.519 |
0.000176 |
26.363 |
| DEMetro_Z |
15 |
4.171 |
0.00156 |
49.256 |
| DEMetro_Z |
18 |
4.759 |
0.000579 |
22.753 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
-0.551
|
0.593
|
-0.159
|
| HMC_vs_DEMetro_Z |
1
|
1.546
|
0.15
|
0.446
|
| HMC_vs_DEMetro_Z |
2
|
-1.239
|
0.241
|
-0.358
|
| HMC_vs_DEMetro_Z |
3
|
2.386
|
0.0361
|
0.689
|
| HMC_vs_DEMetro_Z |
4
|
-0.092
|
0.928
|
-0.027
|
| HMC_vs_DEMetro_Z |
5
|
-2.296
|
0.0423
|
-0.663
|
| Metro_vs_SMC |
0
|
5.719
|
0.000134
|
1.651
|
| Metro_vs_SMC |
1
|
5.399
|
0.000217
|
1.559
|
| Metro_vs_SMC |
2
|
3.406
|
0.00587
|
0.983
|
| Metro_vs_SMC |
3
|
4.985
|
0.000412
|
1.439
|
| Metro_vs_SMC |
4
|
4.920
|
0.000457
|
1.420
|
| Metro_vs_SMC |
5
|
3.804
|
0.00292
|
1.098
|
| Metro_vs_DEMetro_Z |
0
|
1.181
|
0.262
|
0.341
|
| Metro_vs_DEMetro_Z |
1
|
1.472
|
0.169
|
0.425
|
| Metro_vs_DEMetro_Z |
2
|
-0.824
|
0.428
|
-0.238
|
| Metro_vs_DEMetro_Z |
3
|
1.325
|
0.212
|
0.383
|
| Metro_vs_DEMetro_Z |
4
|
-0.059
|
0.954
|
-0.017
|
| Metro_vs_DEMetro_Z |
5
|
-1.870
|
0.0884
|
-0.540
|
| HMC_vs_Metro |
0
|
-1.342
|
0.207
|
-0.387
|
| HMC_vs_Metro |
1
|
-0.361
|
0.725
|
-0.104
|
| HMC_vs_Metro |
2
|
-0.809
|
0.436
|
-0.234
|
| HMC_vs_Metro |
3
|
0.681
|
0.51
|
0.197
|
| HMC_vs_Metro |
4
|
-0.053
|
0.958
|
-0.015
|
| HMC_vs_Metro |
5
|
0.136
|
0.894
|
0.039
|
| HMC_vs_SMC |
0
|
2.954
|
0.0131
|
0.853
|
| HMC_vs_SMC |
1
|
8.063
|
6.06e-06
|
2.328
|
| HMC_vs_SMC |
2
|
3.798
|
0.00295
|
1.096
|
| HMC_vs_SMC |
3
|
5.576
|
0.000166
|
1.610
|
| HMC_vs_SMC |
4
|
3.928
|
0.00236
|
1.134
|
| HMC_vs_SMC |
5
|
3.849
|
0.0027
|
1.111
|
| DEMetro_Z_vs_SMC |
0
|
3.726
|
0.00335
|
1.076
|
| DEMetro_Z_vs_SMC |
1
|
4.481
|
0.000931
|
1.293
|
| DEMetro_Z_vs_SMC |
2
|
3.443
|
0.00549
|
0.994
|
| DEMetro_Z_vs_SMC |
3
|
5.631
|
0.000153
|
1.625
|
| DEMetro_Z_vs_SMC |
4
|
4.136
|
0.00165
|
1.194
|
| DEMetro_Z_vs_SMC |
5
|
4.665
|
0.000688
|
1.347
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
0.526 |
0.034 |
0.018 |
27.607 |
| HMC |
8 |
1.428 |
0.062 |
0.034 |
40.163 |
| HMC |
10 |
1.043 |
0.036 |
0.030 |
33.381 |
| HMC |
12 |
2.303 |
0.063 |
0.053 |
42.519 |
| HMC |
15 |
2.214 |
0.090 |
0.045 |
47.699 |
| HMC |
18 |
1.934 |
0.107 |
0.126 |
14.533 |
| SMC |
5 |
0.038 |
0.034 |
0.018 |
0.206 |
| SMC |
8 |
0.065 |
0.062 |
0.034 |
0.078 |
| SMC |
10 |
0.065 |
0.036 |
0.030 |
0.960 |
| SMC |
12 |
0.064 |
0.063 |
0.053 |
0.018 |
| SMC |
15 |
0.090 |
0.090 |
0.045 |
0.003 |
| SMC |
18 |
0.114 |
0.107 |
0.126 |
0.054 |
| Metro |
5 |
0.892 |
0.034 |
0.018 |
48.150 |
| Metro |
8 |
1.539 |
0.062 |
0.034 |
43.416 |
| Metro |
10 |
1.375 |
0.036 |
0.030 |
44.409 |
| Metro |
12 |
2.011 |
0.063 |
0.053 |
36.972 |
| Metro |
15 |
2.238 |
0.090 |
0.045 |
48.246 |
| Metro |
18 |
1.884 |
0.107 |
0.126 |
14.134 |
| DEMetro_Z |
5 |
0.649 |
0.034 |
0.018 |
34.497 |
| DEMetro_Z |
8 |
1.015 |
0.062 |
0.034 |
28.034 |
| DEMetro_Z |
10 |
1.633 |
0.036 |
0.030 |
52.959 |
| DEMetro_Z |
12 |
1.452 |
0.063 |
0.053 |
26.363 |
| DEMetro_Z |
15 |
2.283 |
0.090 |
0.045 |
49.256 |
| DEMetro_Z |
18 |
2.968 |
0.107 |
0.126 |
22.753 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
2.264 |
0.0447 |
16.427 |
| HMC |
8 |
4.286 |
0.00128 |
40.896 |
| HMC |
10 |
4.148 |
0.00162 |
44.075 |
| HMC |
12 |
3.642 |
0.00388 |
116.792 |
| HMC |
15 |
2.868 |
0.0153 |
89.305 |
| HMC |
18 |
4.038 |
0.00195 |
68.199 |
| SMC |
5 |
-0.226 |
0.823 |
-0.094 |
| SMC |
8 |
1.311 |
0.203 |
0.511 |
| SMC |
10 |
-0.578 |
0.569 |
-0.219 |
| SMC |
12 |
1.011 |
0.323 |
0.396 |
| SMC |
15 |
-0.616 |
0.544 |
-0.245 |
| SMC |
18 |
1.196 |
0.245 |
0.580 |
| Metro |
5 |
3.331 |
0.00668 |
27.812 |
| Metro |
8 |
3.646 |
0.00385 |
56.023 |
| Metro |
10 |
2.733 |
0.0195 |
84.207 |
| Metro |
12 |
3.301 |
0.00706 |
95.351 |
| Metro |
15 |
3.429 |
0.00563 |
77.961 |
| Metro |
18 |
4.276 |
0.00131 |
70.837 |
| DEMetro_Z |
5 |
2.333 |
0.0396 |
19.889 |
| DEMetro_Z |
8 |
3.543 |
0.00459 |
26.399 |
| DEMetro_Z |
10 |
2.857 |
0.0156 |
115.493 |
| DEMetro_Z |
12 |
4.510 |
0.000883 |
42.937 |
| DEMetro_Z |
15 |
2.904 |
0.0144 |
90.031 |
| DEMetro_Z |
18 |
3.158 |
0.00911 |
144.865 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
2.230
|
0.0476
|
0.644
|
| HMC_vs_SMC |
1
|
4.196
|
0.0015
|
1.211
|
| HMC_vs_SMC |
2
|
4.145
|
0.00163
|
1.196
|
| HMC_vs_SMC |
3
|
3.638
|
0.0039
|
1.050
|
| HMC_vs_SMC |
4
|
2.875
|
0.0151
|
0.830
|
| HMC_vs_SMC |
5
|
4.033
|
0.00197
|
1.164
|
| Metro_vs_DEMetro_Z |
0
|
0.658
|
0.524
|
0.190
|
| Metro_vs_DEMetro_Z |
1
|
1.688
|
0.119
|
0.487
|
| Metro_vs_DEMetro_Z |
2
|
-1.109
|
0.291
|
-0.320
|
| Metro_vs_DEMetro_Z |
3
|
2.019
|
0.0685
|
0.583
|
| Metro_vs_DEMetro_Z |
4
|
-0.290
|
0.777
|
-0.084
|
| Metro_vs_DEMetro_Z |
5
|
-1.808
|
0.0981
|
-0.522
|
| HMC_vs_Metro |
0
|
-0.854
|
0.411
|
-0.247
|
| HMC_vs_Metro |
1
|
-0.798
|
0.442
|
-0.230
|
| HMC_vs_Metro |
2
|
-1.372
|
0.197
|
-0.396
|
| HMC_vs_Metro |
3
|
0.638
|
0.536
|
0.184
|
| HMC_vs_Metro |
4
|
0.497
|
0.629
|
0.144
|
| HMC_vs_Metro |
5
|
-0.194
|
0.85
|
-0.056
|
| HMC_vs_DEMetro_Z |
0
|
-0.298
|
0.772
|
-0.086
|
| HMC_vs_DEMetro_Z |
1
|
1.233
|
0.243
|
0.356
|
| HMC_vs_DEMetro_Z |
2
|
-1.819
|
0.0962
|
-0.525
|
| HMC_vs_DEMetro_Z |
3
|
2.497
|
0.0297
|
0.721
|
| HMC_vs_DEMetro_Z |
4
|
-0.015
|
0.988
|
-0.004
|
| HMC_vs_DEMetro_Z |
5
|
-1.952
|
0.0768
|
-0.564
|
| Metro_vs_SMC |
0
|
3.371
|
0.00624
|
0.973
|
| Metro_vs_SMC |
1
|
3.629
|
0.00397
|
1.048
|
| Metro_vs_SMC |
2
|
2.735
|
0.0194
|
0.789
|
| Metro_vs_SMC |
3
|
3.295
|
0.00714
|
0.951
|
| Metro_vs_SMC |
4
|
3.433
|
0.0056
|
0.991
|
| Metro_vs_SMC |
5
|
4.244
|
0.00138
|
1.225
|
| DEMetro_Z_vs_SMC |
0
|
2.361
|
0.0378
|
0.682
|
| DEMetro_Z_vs_SMC |
1
|
3.432
|
0.0056
|
0.991
|
| DEMetro_Z_vs_SMC |
2
|
2.858
|
0.0156
|
0.825
|
| DEMetro_Z_vs_SMC |
3
|
4.466
|
0.000954
|
1.289
|
| DEMetro_Z_vs_SMC |
4
|
2.902
|
0.0144
|
0.838
|
| DEMetro_Z_vs_SMC |
5
|
3.145
|
0.00933
|
0.908
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
0.877 |
0.082 |
0.048 |
16.427 |
| HMC |
8 |
3.317 |
0.088 |
0.079 |
40.896 |
| HMC |
10 |
2.660 |
0.101 |
0.058 |
44.075 |
| HMC |
12 |
10.092 |
0.102 |
0.086 |
116.792 |
| HMC |
15 |
11.692 |
0.187 |
0.129 |
89.305 |
| HMC |
18 |
8.520 |
0.196 |
0.122 |
68.199 |
| SMC |
5 |
0.077 |
0.082 |
0.048 |
-0.094 |
| SMC |
8 |
0.128 |
0.088 |
0.079 |
0.511 |
| SMC |
10 |
0.088 |
0.101 |
0.058 |
-0.219 |
| SMC |
12 |
0.136 |
0.102 |
0.086 |
0.396 |
| SMC |
15 |
0.155 |
0.187 |
0.129 |
-0.245 |
| SMC |
18 |
0.266 |
0.196 |
0.122 |
0.580 |
| Metro |
5 |
1.428 |
0.082 |
0.048 |
27.812 |
| Metro |
8 |
4.511 |
0.088 |
0.079 |
56.023 |
| Metro |
10 |
4.990 |
0.101 |
0.058 |
84.207 |
| Metro |
12 |
8.258 |
0.102 |
0.086 |
95.351 |
| Metro |
15 |
10.231 |
0.187 |
0.129 |
77.961 |
| Metro |
18 |
8.842 |
0.196 |
0.122 |
70.837 |
| DEMetro_Z |
5 |
1.045 |
0.082 |
0.048 |
19.889 |
| DEMetro_Z |
8 |
2.172 |
0.088 |
0.079 |
26.399 |
| DEMetro_Z |
10 |
6.806 |
0.101 |
0.058 |
115.493 |
| DEMetro_Z |
12 |
3.775 |
0.102 |
0.086 |
42.937 |
| DEMetro_Z |
15 |
11.786 |
0.187 |
0.129 |
90.031 |
| DEMetro_Z |
18 |
17.878 |
0.196 |
0.122 |
144.865 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
3.020 |
0.0116 |
31.501 |
| HMC |
8 |
7.674 |
9.35e-06 |
40.456 |
| HMC |
10 |
3.955 |
0.00225 |
43.225 |
| HMC |
12 |
5.337 |
0.000237 |
44.435 |
| HMC |
15 |
3.996 |
0.0021 |
47.971 |
| HMC |
18 |
3.974 |
0.00214 |
17.107 |
| SMC |
5 |
-0.299 |
0.768 |
-0.135 |
| SMC |
8 |
0.278 |
0.784 |
0.122 |
| SMC |
10 |
1.927 |
0.0682 |
0.946 |
| SMC |
12 |
-0.239 |
0.813 |
-0.086 |
| SMC |
15 |
-0.393 |
0.698 |
-0.170 |
| SMC |
18 |
0.283 |
0.78 |
0.109 |
| Metro |
5 |
5.693 |
0.000139 |
54.279 |
| Metro |
8 |
5.612 |
0.000156 |
43.467 |
| Metro |
10 |
3.667 |
0.00371 |
55.313 |
| Metro |
12 |
4.846 |
0.000511 |
38.778 |
| Metro |
15 |
4.998 |
0.000402 |
50.459 |
| Metro |
18 |
4.140 |
0.00161 |
16.676 |
| DEMetro_Z |
5 |
3.620 |
0.00402 |
39.568 |
| DEMetro_Z |
8 |
4.622 |
0.000729 |
28.688 |
| DEMetro_Z |
10 |
3.539 |
0.00464 |
66.304 |
| DEMetro_Z |
12 |
5.581 |
0.000161 |
28.610 |
| DEMetro_Z |
15 |
4.249 |
0.00136 |
50.791 |
| DEMetro_Z |
18 |
4.429 |
0.001 |
27.331 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
1.070
|
0.307
|
0.309
|
| Metro_vs_DEMetro_Z |
1
|
1.470
|
0.17
|
0.424
|
| Metro_vs_DEMetro_Z |
2
|
-0.826
|
0.426
|
-0.238
|
| Metro_vs_DEMetro_Z |
3
|
1.208
|
0.252
|
0.349
|
| Metro_vs_DEMetro_Z |
4
|
-0.019
|
0.985
|
-0.006
|
| Metro_vs_DEMetro_Z |
5
|
-1.834
|
0.0938
|
-0.529
|
| DEMetro_Z_vs_SMC |
0
|
3.682
|
0.00361
|
1.063
|
| DEMetro_Z_vs_SMC |
1
|
4.555
|
0.000823
|
1.315
|
| DEMetro_Z_vs_SMC |
2
|
3.487
|
0.00508
|
1.007
|
| DEMetro_Z_vs_SMC |
3
|
5.675
|
0.000143
|
1.638
|
| DEMetro_Z_vs_SMC |
4
|
4.235
|
0.0014
|
1.222
|
| DEMetro_Z_vs_SMC |
5
|
4.348
|
0.00116
|
1.255
|
| HMC_vs_DEMetro_Z |
0
|
-0.592
|
0.566
|
-0.171
|
| HMC_vs_DEMetro_Z |
1
|
1.506
|
0.16
|
0.435
|
| HMC_vs_DEMetro_Z |
2
|
-1.185
|
0.261
|
-0.342
|
| HMC_vs_DEMetro_Z |
3
|
2.093
|
0.0603
|
0.604
|
| HMC_vs_DEMetro_Z |
4
|
-0.166
|
0.871
|
-0.048
|
| HMC_vs_DEMetro_Z |
5
|
-2.158
|
0.0539
|
-0.623
|
| HMC_vs_Metro |
0
|
-1.299
|
0.22
|
-0.375
|
| HMC_vs_Metro |
1
|
-0.321
|
0.754
|
-0.093
|
| HMC_vs_Metro |
2
|
-0.734
|
0.478
|
-0.212
|
| HMC_vs_Metro |
3
|
0.635
|
0.539
|
0.183
|
| HMC_vs_Metro |
4
|
-0.240
|
0.814
|
-0.069
|
| HMC_vs_Metro |
5
|
0.128
|
0.901
|
0.037
|
| HMC_vs_SMC |
0
|
3.040
|
0.0112
|
0.878
|
| HMC_vs_SMC |
1
|
7.736
|
8.97e-06
|
2.233
|
| HMC_vs_SMC |
2
|
3.845
|
0.00272
|
1.110
|
| HMC_vs_SMC |
3
|
5.438
|
0.000204
|
1.570
|
| HMC_vs_SMC |
4
|
3.990
|
0.00212
|
1.152
|
| HMC_vs_SMC |
5
|
3.832
|
0.00279
|
1.106
|
| Metro_vs_SMC |
0
|
5.702
|
0.000138
|
1.646
|
| Metro_vs_SMC |
1
|
5.455
|
0.000199
|
1.575
|
| Metro_vs_SMC |
2
|
3.581
|
0.00431
|
1.034
|
| Metro_vs_SMC |
3
|
4.898
|
0.000473
|
1.414
|
| Metro_vs_SMC |
4
|
4.979
|
0.000416
|
1.437
|
| Metro_vs_SMC |
5
|
4.002
|
0.00208
|
1.155
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
0.486 |
0.050 |
0.014 |
31.501 |
| HMC |
8 |
1.296 |
0.070 |
0.030 |
40.456 |
| HMC |
10 |
0.974 |
0.052 |
0.021 |
43.225 |
| HMC |
12 |
2.103 |
0.075 |
0.046 |
44.435 |
| HMC |
15 |
1.966 |
0.103 |
0.039 |
47.971 |
| HMC |
18 |
1.773 |
0.114 |
0.097 |
17.107 |
| SMC |
5 |
0.048 |
0.050 |
0.014 |
-0.135 |
| SMC |
8 |
0.073 |
0.070 |
0.030 |
0.122 |
| SMC |
10 |
0.072 |
0.052 |
0.021 |
0.946 |
| SMC |
12 |
0.071 |
0.075 |
0.046 |
-0.086 |
| SMC |
15 |
0.097 |
0.103 |
0.039 |
-0.170 |
| SMC |
18 |
0.125 |
0.114 |
0.097 |
0.109 |
| Metro |
5 |
0.801 |
0.050 |
0.014 |
54.279 |
| Metro |
8 |
1.387 |
0.070 |
0.030 |
43.467 |
| Metro |
10 |
1.232 |
0.052 |
0.021 |
55.313 |
| Metro |
12 |
1.845 |
0.075 |
0.046 |
38.778 |
| Metro |
15 |
2.063 |
0.103 |
0.039 |
50.459 |
| Metro |
18 |
1.732 |
0.114 |
0.097 |
16.676 |
| DEMetro_Z |
5 |
0.598 |
0.050 |
0.014 |
39.568 |
| DEMetro_Z |
8 |
0.939 |
0.070 |
0.030 |
28.688 |
| DEMetro_Z |
10 |
1.466 |
0.052 |
0.021 |
66.304 |
| DEMetro_Z |
12 |
1.381 |
0.075 |
0.046 |
28.610 |
| DEMetro_Z |
15 |
2.076 |
0.103 |
0.039 |
50.791 |
| DEMetro_Z |
18 |
2.765 |
0.114 |
0.097 |
27.331 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
2.939 |
0.0134 |
30.824 |
| HMC |
8 |
7.993 |
6.37e-06 |
44.238 |
| HMC |
10 |
3.962 |
0.00222 |
43.382 |
| HMC |
12 |
5.666 |
0.000144 |
47.080 |
| HMC |
15 |
4.050 |
0.00191 |
60.356 |
| HMC |
18 |
3.992 |
0.00208 |
18.660 |
| SMC |
5 |
-0.099 |
0.922 |
-0.042 |
| SMC |
8 |
0.387 |
0.703 |
0.175 |
| SMC |
10 |
2.089 |
0.0493 |
0.987 |
| SMC |
12 |
-0.105 |
0.918 |
-0.037 |
| SMC |
15 |
-0.203 |
0.841 |
-0.092 |
| SMC |
18 |
0.268 |
0.792 |
0.103 |
| Metro |
5 |
5.332 |
0.000239 |
53.222 |
| Metro |
8 |
5.555 |
0.00017 |
47.437 |
| Metro |
10 |
3.719 |
0.00338 |
57.580 |
| Metro |
12 |
5.051 |
0.000368 |
40.300 |
| Metro |
15 |
5.051 |
0.00037 |
61.198 |
| Metro |
18 |
4.122 |
0.00167 |
19.046 |
| DEMetro_Z |
5 |
3.523 |
0.00476 |
39.916 |
| DEMetro_Z |
8 |
4.510 |
0.000878 |
30.827 |
| DEMetro_Z |
10 |
3.535 |
0.00467 |
65.750 |
| DEMetro_Z |
12 |
5.495 |
0.000184 |
30.064 |
| DEMetro_Z |
15 |
4.377 |
0.0011 |
61.755 |
| DEMetro_Z |
18 |
4.872 |
0.000487 |
28.965 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
3.561
|
0.00446
|
1.028
|
| DEMetro_Z_vs_SMC |
1
|
4.470
|
0.000947
|
1.290
|
| DEMetro_Z_vs_SMC |
2
|
3.476
|
0.00518
|
1.003
|
| DEMetro_Z_vs_SMC |
3
|
5.583
|
0.000164
|
1.612
|
| DEMetro_Z_vs_SMC |
4
|
4.356
|
0.00114
|
1.257
|
| DEMetro_Z_vs_SMC |
5
|
4.776
|
0.000575
|
1.379
|
| HMC_vs_Metro |
0
|
-1.276
|
0.228
|
-0.368
|
| HMC_vs_Metro |
1
|
-0.315
|
0.758
|
-0.091
|
| HMC_vs_Metro |
2
|
-0.846
|
0.416
|
-0.244
|
| HMC_vs_Metro |
3
|
0.779
|
0.453
|
0.225
|
| HMC_vs_Metro |
4
|
-0.064
|
0.95
|
-0.019
|
| HMC_vs_Metro |
5
|
-0.108
|
0.916
|
-0.031
|
| Metro_vs_DEMetro_Z |
0
|
0.969
|
0.354
|
0.280
|
| Metro_vs_DEMetro_Z |
1
|
1.415
|
0.185
|
0.409
|
| Metro_vs_DEMetro_Z |
2
|
-0.621
|
0.547
|
-0.179
|
| Metro_vs_DEMetro_Z |
3
|
1.183
|
0.262
|
0.342
|
| Metro_vs_DEMetro_Z |
4
|
-0.027
|
0.979
|
-0.008
|
| Metro_vs_DEMetro_Z |
5
|
-1.741
|
0.11
|
-0.503
|
| HMC_vs_SMC |
0
|
2.932
|
0.0136
|
0.846
|
| HMC_vs_SMC |
1
|
8.025
|
6.34e-06
|
2.317
|
| HMC_vs_SMC |
2
|
3.837
|
0.00276
|
1.108
|
| HMC_vs_SMC |
3
|
5.750
|
0.000128
|
1.660
|
| HMC_vs_SMC |
4
|
4.037
|
0.00196
|
1.165
|
| HMC_vs_SMC |
5
|
3.842
|
0.00273
|
1.109
|
| Metro_vs_SMC |
0
|
5.349
|
0.000234
|
1.544
|
| Metro_vs_SMC |
1
|
5.402
|
0.000216
|
1.559
|
| Metro_vs_SMC |
2
|
3.635
|
0.00392
|
1.049
|
| Metro_vs_SMC |
3
|
5.089
|
0.00035
|
1.469
|
| Metro_vs_SMC |
4
|
5.044
|
0.000376
|
1.456
|
| Metro_vs_SMC |
5
|
4.001
|
0.00208
|
1.155
|
| HMC_vs_DEMetro_Z |
0
|
-0.611
|
0.554
|
-0.176
|
| HMC_vs_DEMetro_Z |
1
|
1.560
|
0.147
|
0.450
|
| HMC_vs_DEMetro_Z |
2
|
-1.141
|
0.278
|
-0.329
|
| HMC_vs_DEMetro_Z |
3
|
2.337
|
0.0394
|
0.675
|
| HMC_vs_DEMetro_Z |
4
|
-0.069
|
0.946
|
-0.020
|
| HMC_vs_DEMetro_Z |
5
|
-2.290
|
0.0428
|
-0.661
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
0.156 |
0.013 |
0.005 |
30.824 |
| HMC |
8 |
0.311 |
0.013 |
0.007 |
44.238 |
| HMC |
10 |
0.193 |
0.007 |
0.004 |
43.382 |
| HMC |
12 |
0.350 |
0.009 |
0.007 |
47.080 |
| HMC |
15 |
0.272 |
0.010 |
0.004 |
60.356 |
| HMC |
18 |
0.199 |
0.010 |
0.010 |
18.660 |
| SMC |
5 |
0.013 |
0.013 |
0.005 |
-0.042 |
| SMC |
8 |
0.014 |
0.013 |
0.007 |
0.175 |
| SMC |
10 |
0.011 |
0.007 |
0.004 |
0.987 |
| SMC |
12 |
0.009 |
0.009 |
0.007 |
-0.037 |
| SMC |
15 |
0.010 |
0.010 |
0.004 |
-0.092 |
| SMC |
18 |
0.011 |
0.010 |
0.010 |
0.103 |
| Metro |
5 |
0.260 |
0.013 |
0.005 |
53.222 |
| Metro |
8 |
0.333 |
0.013 |
0.007 |
47.437 |
| Metro |
10 |
0.254 |
0.007 |
0.004 |
57.580 |
| Metro |
12 |
0.301 |
0.009 |
0.007 |
40.300 |
| Metro |
15 |
0.276 |
0.010 |
0.004 |
61.198 |
| Metro |
18 |
0.202 |
0.010 |
0.010 |
19.046 |
| DEMetro_Z |
5 |
0.198 |
0.013 |
0.005 |
39.916 |
| DEMetro_Z |
8 |
0.221 |
0.013 |
0.007 |
30.827 |
| DEMetro_Z |
10 |
0.289 |
0.007 |
0.004 |
65.750 |
| DEMetro_Z |
12 |
0.227 |
0.009 |
0.007 |
30.064 |
| DEMetro_Z |
15 |
0.278 |
0.010 |
0.004 |
61.755 |
| DEMetro_Z |
18 |
0.303 |
0.010 |
0.010 |
28.965 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
R Hat (scatter)
Mode Transitions
One Chain results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
138.598 |
3.45e-25 |
96.869 |
| HMC |
8 |
137.242 |
1.06e-27 |
81.064 |
| HMC |
10 |
197.817 |
2.09e-30 |
117.075 |
| HMC |
12 |
169.349 |
4.84e-34 |
79.724 |
| HMC |
15 |
198.648 |
1.72e-30 |
117.248 |
| HMC |
18 |
115.503 |
6.99e-32 |
49.587 |
| SMC |
5 |
-0.436 |
0.667 |
-0.174 |
| SMC |
8 |
0.326 |
0.748 |
0.170 |
| SMC |
10 |
1.904 |
0.0709 |
0.905 |
| SMC |
12 |
0.595 |
0.558 |
0.212 |
| SMC |
15 |
0.479 |
0.637 |
0.203 |
| SMC |
18 |
-0.639 |
0.533 |
-0.197 |
| Metro |
5 |
5.061 |
0.000364 |
55.186 |
| Metro |
8 |
124.642 |
1.75e-25 |
80.895 |
| Metro |
10 |
132.262 |
1.75e-22 |
117.630 |
| Metro |
12 |
158.892 |
3.84e-32 |
79.760 |
| Metro |
15 |
238.754 |
5.87e-36 |
118.234 |
| Metro |
18 |
130.077 |
1.11e-32 |
49.602 |
| DEMetro_Z |
5 |
4.356 |
0.00114 |
59.925 |
| DEMetro_Z |
8 |
7.437 |
1.28e-05 |
67.148 |
| DEMetro_Z |
10 |
161.319 |
9.13e-26 |
116.536 |
| DEMetro_Z |
12 |
149.952 |
1.16e-30 |
78.874 |
| DEMetro_Z |
15 |
209.535 |
7.03e-32 |
118.010 |
| DEMetro_Z |
18 |
115.919 |
6.29e-32 |
49.696 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
2.708
|
0.0204
|
0.782
|
| HMC_vs_DEMetro_Z |
1
|
1.526
|
0.155
|
0.440
|
| HMC_vs_DEMetro_Z |
2
|
0.678
|
0.512
|
0.196
|
| HMC_vs_DEMetro_Z |
3
|
1.352
|
0.203
|
0.390
|
| HMC_vs_DEMetro_Z |
4
|
-1.227
|
0.245
|
-0.354
|
| HMC_vs_DEMetro_Z |
5
|
-0.312
|
0.761
|
-0.090
|
| Metro_vs_SMC |
0
|
5.028
|
0.000385
|
1.451
|
| Metro_vs_SMC |
1
|
90.236
|
3.86e-17
|
26.049
|
| Metro_vs_SMC |
2
|
126.758
|
9.22e-19
|
36.592
|
| Metro_vs_SMC |
3
|
220.509
|
2.09e-21
|
63.655
|
| Metro_vs_SMC |
4
|
231.065
|
1.25e-21
|
66.703
|
| Metro_vs_SMC |
5
|
181.820
|
1.75e-20
|
52.487
|
| Metro_vs_DEMetro_Z |
0
|
-0.243
|
0.813
|
-0.070
|
| Metro_vs_DEMetro_Z |
1
|
1.517
|
0.158
|
0.438
|
| Metro_vs_DEMetro_Z |
2
|
1.116
|
0.288
|
0.322
|
| Metro_vs_DEMetro_Z |
3
|
1.187
|
0.26
|
0.343
|
| Metro_vs_DEMetro_Z |
4
|
0.444
|
0.665
|
0.128
|
| Metro_vs_DEMetro_Z |
5
|
-0.316
|
0.758
|
-0.091
|
| HMC_vs_Metro |
0
|
3.750
|
0.00321
|
1.083
|
| HMC_vs_Metro |
1
|
0.268
|
0.794
|
0.077
|
| HMC_vs_Metro |
2
|
-0.546
|
0.596
|
-0.158
|
| HMC_vs_Metro |
3
|
-0.102
|
0.92
|
-0.030
|
| HMC_vs_Metro |
4
|
-2.484
|
0.0303
|
-0.717
|
| HMC_vs_Metro |
5
|
-0.085
|
0.934
|
-0.024
|
| HMC_vs_SMC |
0
|
136.925
|
3.95e-19
|
39.527
|
| HMC_vs_SMC |
1
|
98.957
|
1.4e-17
|
28.566
|
| HMC_vs_SMC |
2
|
201.189
|
5.74e-21
|
58.078
|
| HMC_vs_SMC |
3
|
257.620
|
3.78e-22
|
74.368
|
| HMC_vs_SMC |
4
|
206.033
|
4.42e-21
|
59.477
|
| HMC_vs_SMC |
5
|
143.878
|
2.29e-19
|
41.534
|
| DEMetro_Z_vs_SMC |
0
|
4.376
|
0.00111
|
1.263
|
| DEMetro_Z_vs_SMC |
1
|
7.354
|
1.44e-05
|
2.123
|
| DEMetro_Z_vs_SMC |
2
|
177.861
|
2.23e-20
|
51.344
|
| DEMetro_Z_vs_SMC |
3
|
155.956
|
9.44e-20
|
45.021
|
| DEMetro_Z_vs_SMC |
4
|
179.952
|
1.96e-20
|
51.948
|
| DEMetro_Z_vs_SMC |
5
|
140.099
|
3.07e-19
|
40.443
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
1.760 |
0.034 |
0.018 |
96.869 |
| HMC |
8 |
2.819 |
0.062 |
0.034 |
81.064 |
| HMC |
10 |
3.567 |
0.036 |
0.030 |
117.075 |
| HMC |
12 |
4.262 |
0.063 |
0.053 |
79.724 |
| HMC |
15 |
5.310 |
0.090 |
0.045 |
117.248 |
| HMC |
18 |
6.342 |
0.107 |
0.126 |
49.587 |
| SMC |
5 |
0.031 |
0.034 |
0.018 |
-0.174 |
| SMC |
8 |
0.068 |
0.062 |
0.034 |
0.170 |
| SMC |
10 |
0.063 |
0.036 |
0.030 |
0.905 |
| SMC |
12 |
0.074 |
0.063 |
0.053 |
0.212 |
| SMC |
15 |
0.099 |
0.090 |
0.045 |
0.203 |
| SMC |
18 |
0.082 |
0.107 |
0.126 |
-0.197 |
| Metro |
5 |
1.017 |
0.034 |
0.018 |
55.186 |
| Metro |
8 |
2.813 |
0.062 |
0.034 |
80.895 |
| Metro |
10 |
3.583 |
0.036 |
0.030 |
117.630 |
| Metro |
12 |
4.264 |
0.063 |
0.053 |
79.760 |
| Metro |
15 |
5.354 |
0.090 |
0.045 |
118.234 |
| Metro |
18 |
6.344 |
0.107 |
0.126 |
49.602 |
| DEMetro_Z |
5 |
1.102 |
0.034 |
0.018 |
59.925 |
| DEMetro_Z |
8 |
2.346 |
0.062 |
0.034 |
67.148 |
| DEMetro_Z |
10 |
3.550 |
0.036 |
0.030 |
116.536 |
| DEMetro_Z |
12 |
4.218 |
0.063 |
0.053 |
78.874 |
| DEMetro_Z |
15 |
5.344 |
0.090 |
0.045 |
118.010 |
| DEMetro_Z |
18 |
6.355 |
0.107 |
0.126 |
49.696 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
187.014 |
1.22e-34 |
89.281 |
| HMC |
8 |
382.847 |
9.18e-42 |
141.272 |
| HMC |
10 |
468.154 |
7.76e-35 |
302.460 |
| HMC |
12 |
495.662 |
4.64e-37 |
296.043 |
| HMC |
15 |
767.288 |
3.87e-50 |
307.419 |
| HMC |
18 |
1058.120 |
2.78e-52 |
467.556 |
| SMC |
5 |
-0.570 |
0.575 |
-0.210 |
| SMC |
8 |
0.153 |
0.88 |
0.057 |
| SMC |
10 |
0.195 |
0.847 |
0.080 |
| SMC |
12 |
1.094 |
0.287 |
0.550 |
| SMC |
15 |
0.488 |
0.631 |
0.171 |
| SMC |
18 |
0.664 |
0.514 |
0.319 |
| Metro |
5 |
4.063 |
0.00187 |
41.817 |
| Metro |
8 |
306.324 |
9.49e-40 |
141.877 |
| Metro |
10 |
468.775 |
6.99e-35 |
302.347 |
| Metro |
12 |
497.398 |
3.63e-37 |
296.125 |
| Metro |
15 |
676.422 |
1.89e-47 |
307.450 |
| Metro |
18 |
905.063 |
4.36e-46 |
467.624 |
| DEMetro_Z |
5 |
4.032 |
0.00197 |
53.078 |
| DEMetro_Z |
8 |
7.355 |
1.43e-05 |
115.470 |
| DEMetro_Z |
10 |
451.445 |
7.93e-34 |
302.723 |
| DEMetro_Z |
12 |
552.403 |
7.08e-41 |
295.924 |
| DEMetro_Z |
15 |
715.816 |
3.85e-49 |
307.381 |
| DEMetro_Z |
18 |
1016.327 |
7.25e-51 |
467.470 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
209.543
|
3.67e-21
|
60.490
|
| HMC_vs_SMC |
1
|
342.574
|
1.65e-23
|
98.892
|
| HMC_vs_SMC |
2
|
408.453
|
2.38e-24
|
117.910
|
| HMC_vs_SMC |
3
|
344.941
|
1.53e-23
|
99.576
|
| HMC_vs_SMC |
4
|
828.011
|
1e-27
|
239.026
|
| HMC_vs_SMC |
5
|
1155.207
|
2.57e-29
|
333.480
|
| Metro_vs_DEMetro_Z |
0
|
-0.606
|
0.557
|
-0.175
|
| Metro_vs_DEMetro_Z |
1
|
1.693
|
0.119
|
0.489
|
| Metro_vs_DEMetro_Z |
2
|
-0.922
|
0.376
|
-0.266
|
| Metro_vs_DEMetro_Z |
3
|
0.792
|
0.445
|
0.229
|
| Metro_vs_DEMetro_Z |
4
|
0.341
|
0.74
|
0.098
|
| Metro_vs_DEMetro_Z |
5
|
0.551
|
0.593
|
0.159
|
| HMC_vs_Metro |
0
|
4.553
|
0.000826
|
1.314
|
| HMC_vs_Metro |
1
|
-2.347
|
0.0387
|
-0.677
|
| HMC_vs_Metro |
2
|
0.282
|
0.783
|
0.081
|
| HMC_vs_Metro |
3
|
-0.379
|
0.712
|
-0.109
|
| HMC_vs_Metro |
4
|
-0.167
|
0.871
|
-0.048
|
| HMC_vs_Metro |
5
|
-0.298
|
0.772
|
-0.086
|
| HMC_vs_DEMetro_Z |
0
|
2.801
|
0.0172
|
0.809
|
| HMC_vs_DEMetro_Z |
1
|
1.645
|
0.128
|
0.475
|
| HMC_vs_DEMetro_Z |
2
|
-0.962
|
0.356
|
-0.278
|
| HMC_vs_DEMetro_Z |
3
|
0.566
|
0.583
|
0.163
|
| HMC_vs_DEMetro_Z |
4
|
0.317
|
0.757
|
0.092
|
| HMC_vs_DEMetro_Z |
5
|
0.736
|
0.477
|
0.213
|
| Metro_vs_SMC |
0
|
4.145
|
0.00163
|
1.197
|
| Metro_vs_SMC |
1
|
255.251
|
4.19e-22
|
73.685
|
| Metro_vs_SMC |
2
|
405.778
|
2.56e-24
|
117.138
|
| Metro_vs_SMC |
3
|
345.618
|
1.49e-23
|
99.771
|
| Metro_vs_SMC |
4
|
742.804
|
3.31e-27
|
214.429
|
| Metro_vs_SMC |
5
|
1005.076
|
1.19e-28
|
290.141
|
| DEMetro_Z_vs_SMC |
0
|
4.046
|
0.00193
|
1.168
|
| DEMetro_Z_vs_SMC |
1
|
7.326
|
1.49e-05
|
2.115
|
| DEMetro_Z_vs_SMC |
2
|
362.726
|
8.78e-24
|
104.710
|
| DEMetro_Z_vs_SMC |
3
|
381.113
|
5.1e-24
|
110.018
|
| DEMetro_Z_vs_SMC |
4
|
759.844
|
2.58e-27
|
219.348
|
| DEMetro_Z_vs_SMC |
5
|
993.522
|
1.35e-28
|
286.805
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
4.405 |
0.082 |
0.048 |
89.281 |
| HMC |
8 |
11.242 |
0.088 |
0.079 |
141.272 |
| HMC |
10 |
17.660 |
0.101 |
0.058 |
302.460 |
| HMC |
12 |
25.424 |
0.102 |
0.086 |
296.043 |
| HMC |
15 |
39.793 |
0.187 |
0.129 |
307.419 |
| HMC |
18 |
57.267 |
0.196 |
0.122 |
467.556 |
| SMC |
5 |
0.072 |
0.082 |
0.048 |
-0.210 |
| SMC |
8 |
0.093 |
0.088 |
0.079 |
0.057 |
| SMC |
10 |
0.106 |
0.101 |
0.058 |
0.080 |
| SMC |
12 |
0.149 |
0.102 |
0.086 |
0.550 |
| SMC |
15 |
0.209 |
0.187 |
0.129 |
0.171 |
| SMC |
18 |
0.235 |
0.196 |
0.122 |
0.319 |
| Metro |
5 |
2.107 |
0.082 |
0.048 |
41.817 |
| Metro |
8 |
11.290 |
0.088 |
0.079 |
141.877 |
| Metro |
10 |
17.654 |
0.101 |
0.058 |
302.347 |
| Metro |
12 |
25.431 |
0.102 |
0.086 |
296.125 |
| Metro |
15 |
39.797 |
0.187 |
0.129 |
307.450 |
| Metro |
18 |
57.275 |
0.196 |
0.122 |
467.624 |
| DEMetro_Z |
5 |
2.652 |
0.082 |
0.048 |
53.078 |
| DEMetro_Z |
8 |
9.205 |
0.088 |
0.079 |
115.470 |
| DEMetro_Z |
10 |
17.675 |
0.101 |
0.058 |
302.723 |
| DEMetro_Z |
12 |
25.414 |
0.102 |
0.086 |
295.924 |
| DEMetro_Z |
15 |
39.788 |
0.187 |
0.129 |
307.381 |
| DEMetro_Z |
18 |
57.256 |
0.196 |
0.122 |
467.470 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
56.130 |
2.34e-15 |
112.172 |
| HMC |
8 |
60.328 |
2.35e-16 |
80.448 |
| HMC |
10 |
40.122 |
2.13e-13 |
149.553 |
| HMC |
12 |
37.066 |
3.04e-13 |
79.979 |
| HMC |
15 |
38.014 |
3.4e-13 |
115.985 |
| HMC |
18 |
34.979 |
3.32e-13 |
57.417 |
| SMC |
5 |
-1.393 |
0.178 |
-0.523 |
| SMC |
8 |
0.150 |
0.882 |
0.072 |
| SMC |
10 |
1.672 |
0.11 |
0.842 |
| SMC |
12 |
0.421 |
0.679 |
0.147 |
| SMC |
15 |
-0.062 |
0.951 |
-0.025 |
| SMC |
18 |
-0.695 |
0.498 |
-0.220 |
| Metro |
5 |
5.029 |
0.000384 |
64.126 |
| Metro |
8 |
42.236 |
5.82e-14 |
83.063 |
| Metro |
10 |
37.634 |
4.53e-13 |
154.093 |
| Metro |
12 |
68.819 |
1.79e-17 |
79.169 |
| Metro |
15 |
51.698 |
7.52e-15 |
116.301 |
| Metro |
18 |
53.565 |
2.38e-16 |
57.478 |
| DEMetro_Z |
5 |
4.394 |
0.00107 |
70.757 |
| DEMetro_Z |
8 |
7.271 |
1.58e-05 |
65.234 |
| DEMetro_Z |
10 |
53.942 |
5.96e-15 |
143.807 |
| DEMetro_Z |
12 |
61.841 |
1.6e-16 |
81.203 |
| DEMetro_Z |
15 |
45.654 |
3.88e-14 |
121.905 |
| DEMetro_Z |
18 |
45.707 |
5.2e-15 |
58.064 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
-0.298
|
0.772
|
-0.086
|
| Metro_vs_DEMetro_Z |
1
|
1.841
|
0.0927
|
0.531
|
| Metro_vs_DEMetro_Z |
2
|
2.528
|
0.0281
|
0.730
|
| Metro_vs_DEMetro_Z |
3
|
-1.375
|
0.196
|
-0.397
|
| Metro_vs_DEMetro_Z |
4
|
-2.350
|
0.0385
|
-0.678
|
| Metro_vs_DEMetro_Z |
5
|
-0.372
|
0.717
|
-0.107
|
| DEMetro_Z_vs_SMC |
0
|
4.432
|
0.00101
|
1.279
|
| DEMetro_Z_vs_SMC |
1
|
7.209
|
1.73e-05
|
2.081
|
| DEMetro_Z_vs_SMC |
2
|
53.530
|
1.19e-14
|
15.453
|
| DEMetro_Z_vs_SMC |
3
|
59.628
|
3.65e-15
|
17.213
|
| DEMetro_Z_vs_SMC |
4
|
44.571
|
8.86e-14
|
12.867
|
| DEMetro_Z_vs_SMC |
5
|
48.028
|
3.91e-14
|
13.864
|
| HMC_vs_DEMetro_Z |
0
|
2.659
|
0.0222
|
0.768
|
| HMC_vs_DEMetro_Z |
1
|
1.703
|
0.117
|
0.492
|
| HMC_vs_DEMetro_Z |
2
|
1.102
|
0.294
|
0.318
|
| HMC_vs_DEMetro_Z |
3
|
-0.498
|
0.628
|
-0.144
|
| HMC_vs_DEMetro_Z |
4
|
-1.244
|
0.239
|
-0.359
|
| HMC_vs_DEMetro_Z |
5
|
-0.322
|
0.753
|
-0.093
|
| HMC_vs_Metro |
0
|
3.695
|
0.00353
|
1.067
|
| HMC_vs_Metro |
1
|
-1.021
|
0.329
|
-0.295
|
| HMC_vs_Metro |
2
|
-0.701
|
0.498
|
-0.202
|
| HMC_vs_Metro |
3
|
0.318
|
0.757
|
0.092
|
| HMC_vs_Metro |
4
|
-0.071
|
0.944
|
-0.021
|
| HMC_vs_Metro |
5
|
-0.033
|
0.974
|
-0.009
|
| HMC_vs_SMC |
0
|
53.718
|
1.15e-14
|
15.507
|
| HMC_vs_SMC |
1
|
67.993
|
8.64e-16
|
19.628
|
| HMC_vs_SMC |
2
|
38.306
|
4.64e-13
|
11.058
|
| HMC_vs_SMC |
3
|
37.540
|
5.79e-13
|
10.837
|
| HMC_vs_SMC |
4
|
37.341
|
6.13e-13
|
10.779
|
| HMC_vs_SMC |
5
|
34.384
|
1.51e-12
|
9.926
|
| Metro_vs_SMC |
0
|
5.042
|
0.000377
|
1.456
|
| Metro_vs_SMC |
1
|
38.609
|
4.26e-13
|
11.145
|
| Metro_vs_SMC |
2
|
36.131
|
8.79e-13
|
10.430
|
| Metro_vs_SMC |
3
|
68.274
|
8.26e-16
|
19.709
|
| Metro_vs_SMC |
4
|
52.214
|
1.57e-14
|
15.073
|
| Metro_vs_SMC |
5
|
57.802
|
5.13e-15
|
16.686
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
1.603 |
0.050 |
0.014 |
112.172 |
| HMC |
8 |
2.508 |
0.070 |
0.030 |
80.448 |
| HMC |
10 |
3.241 |
0.052 |
0.021 |
149.553 |
| HMC |
12 |
3.725 |
0.075 |
0.046 |
79.979 |
| HMC |
15 |
4.607 |
0.103 |
0.039 |
115.985 |
| HMC |
18 |
5.683 |
0.114 |
0.097 |
57.417 |
| SMC |
5 |
0.042 |
0.050 |
0.014 |
-0.523 |
| SMC |
8 |
0.072 |
0.070 |
0.030 |
0.072 |
| SMC |
10 |
0.070 |
0.052 |
0.021 |
0.842 |
| SMC |
12 |
0.082 |
0.075 |
0.046 |
0.147 |
| SMC |
15 |
0.102 |
0.103 |
0.039 |
-0.025 |
| SMC |
18 |
0.093 |
0.114 |
0.097 |
-0.220 |
| Metro |
5 |
0.938 |
0.050 |
0.014 |
64.126 |
| Metro |
8 |
2.587 |
0.070 |
0.030 |
83.063 |
| Metro |
10 |
3.338 |
0.052 |
0.021 |
154.093 |
| Metro |
12 |
3.688 |
0.075 |
0.046 |
79.169 |
| Metro |
15 |
4.620 |
0.103 |
0.039 |
116.301 |
| Metro |
18 |
5.689 |
0.114 |
0.097 |
57.478 |
| DEMetro_Z |
5 |
1.030 |
0.050 |
0.014 |
70.757 |
| DEMetro_Z |
8 |
2.046 |
0.070 |
0.030 |
65.234 |
| DEMetro_Z |
10 |
3.118 |
0.052 |
0.021 |
143.807 |
| DEMetro_Z |
12 |
3.781 |
0.075 |
0.046 |
81.203 |
| DEMetro_Z |
15 |
4.837 |
0.103 |
0.039 |
121.905 |
| DEMetro_Z |
18 |
5.746 |
0.114 |
0.097 |
58.064 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
146.715 |
3.04e-24 |
114.830 |
| HMC |
8 |
66.898 |
6.5e-17 |
88.555 |
| HMC |
10 |
86.498 |
9.51e-18 |
145.283 |
| HMC |
12 |
130.369 |
1.45e-25 |
85.960 |
| HMC |
15 |
106.048 |
2.66e-19 |
141.787 |
| HMC |
18 |
112.906 |
4e-28 |
60.022 |
| SMC |
5 |
-1.310 |
0.204 |
-0.495 |
| SMC |
8 |
0.177 |
0.861 |
0.086 |
| SMC |
10 |
1.555 |
0.136 |
0.772 |
| SMC |
12 |
0.588 |
0.563 |
0.206 |
| SMC |
15 |
0.997 |
0.33 |
0.450 |
| SMC |
18 |
-0.242 |
0.812 |
-0.078 |
| Metro |
5 |
4.875 |
0.000489 |
61.934 |
| Metro |
8 |
94.274 |
5.11e-20 |
90.554 |
| Metro |
10 |
162.731 |
1.12e-23 |
145.183 |
| Metro |
12 |
110.952 |
1.43e-22 |
86.192 |
| Metro |
15 |
118.478 |
3.59e-20 |
145.046 |
| Metro |
18 |
79.674 |
1.15e-20 |
60.712 |
| DEMetro_Z |
5 |
4.391 |
0.00108 |
70.131 |
| DEMetro_Z |
8 |
7.404 |
1.34e-05 |
73.928 |
| DEMetro_Z |
10 |
78.721 |
3.78e-17 |
143.702 |
| DEMetro_Z |
12 |
98.183 |
7.25e-21 |
85.652 |
| DEMetro_Z |
15 |
91.256 |
3.54e-18 |
140.684 |
| DEMetro_Z |
18 |
77.318 |
2.88e-20 |
60.369 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
4.421
|
0.00103
|
1.276
|
| DEMetro_Z_vs_SMC |
1
|
7.355
|
1.44e-05
|
2.123
|
| DEMetro_Z_vs_SMC |
2
|
87.084
|
5.71e-17
|
25.139
|
| DEMetro_Z_vs_SMC |
3
|
98.606
|
1.46e-17
|
28.465
|
| DEMetro_Z_vs_SMC |
4
|
94.346
|
2.37e-17
|
27.235
|
| DEMetro_Z_vs_SMC |
5
|
75.868
|
2.6e-16
|
21.901
|
| HMC_vs_Metro |
0
|
4.186
|
0.00152
|
1.208
|
| HMC_vs_Metro |
1
|
-1.870
|
0.0883
|
-0.540
|
| HMC_vs_Metro |
2
|
0.061
|
0.953
|
0.018
|
| HMC_vs_Metro |
3
|
-0.342
|
0.739
|
-0.099
|
| HMC_vs_Metro |
4
|
-2.160
|
0.0537
|
-0.624
|
| HMC_vs_Metro |
5
|
-1.026
|
0.327
|
-0.296
|
| Metro_vs_DEMetro_Z |
0
|
-0.364
|
0.723
|
-0.105
|
| Metro_vs_DEMetro_Z |
1
|
1.631
|
0.131
|
0.471
|
| Metro_vs_DEMetro_Z |
2
|
0.895
|
0.39
|
0.258
|
| Metro_vs_DEMetro_Z |
3
|
0.490
|
0.634
|
0.142
|
| Metro_vs_DEMetro_Z |
4
|
3.024
|
0.0116
|
0.873
|
| Metro_vs_DEMetro_Z |
5
|
0.386
|
0.707
|
0.111
|
| HMC_vs_SMC |
0
|
130.412
|
6.75e-19
|
37.647
|
| HMC_vs_SMC |
1
|
60.898
|
2.9e-15
|
17.580
|
| HMC_vs_SMC |
2
|
98.614
|
1.46e-17
|
28.467
|
| HMC_vs_SMC |
3
|
158.907
|
7.68e-20
|
45.873
|
| HMC_vs_SMC |
4
|
115.229
|
2.63e-18
|
33.264
|
| HMC_vs_SMC |
5
|
115.117
|
2.66e-18
|
33.232
|
| Metro_vs_SMC |
0
|
4.892
|
0.000478
|
1.412
|
| Metro_vs_SMC |
1
|
75.569
|
2.71e-16
|
21.815
|
| Metro_vs_SMC |
2
|
179.365
|
2.03e-20
|
51.778
|
| Metro_vs_SMC |
3
|
138.916
|
3.37e-19
|
40.102
|
| Metro_vs_SMC |
4
|
117.716
|
2.08e-18
|
33.982
|
| Metro_vs_SMC |
5
|
90.087
|
3.93e-17
|
26.006
|
| HMC_vs_DEMetro_Z |
0
|
2.784
|
0.0178
|
0.804
|
| HMC_vs_DEMetro_Z |
1
|
1.349
|
0.204
|
0.389
|
| HMC_vs_DEMetro_Z |
2
|
0.689
|
0.505
|
0.199
|
| HMC_vs_DEMetro_Z |
3
|
0.282
|
0.783
|
0.081
|
| HMC_vs_DEMetro_Z |
4
|
0.603
|
0.559
|
0.174
|
| HMC_vs_DEMetro_Z |
5
|
-0.544
|
0.597
|
-0.157
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
0.545 |
0.013 |
0.005 |
114.830 |
| HMC |
8 |
0.610 |
0.013 |
0.007 |
88.555 |
| HMC |
10 |
0.630 |
0.007 |
0.004 |
145.283 |
| HMC |
12 |
0.631 |
0.009 |
0.007 |
85.960 |
| HMC |
15 |
0.626 |
0.010 |
0.004 |
141.787 |
| HMC |
18 |
0.616 |
0.010 |
0.010 |
60.022 |
| SMC |
5 |
0.011 |
0.013 |
0.005 |
-0.495 |
| SMC |
8 |
0.013 |
0.013 |
0.007 |
0.086 |
| SMC |
10 |
0.010 |
0.007 |
0.004 |
0.772 |
| SMC |
12 |
0.011 |
0.009 |
0.007 |
0.206 |
| SMC |
15 |
0.012 |
0.010 |
0.004 |
0.450 |
| SMC |
18 |
0.009 |
0.010 |
0.010 |
-0.078 |
| Metro |
5 |
0.300 |
0.013 |
0.005 |
61.934 |
| Metro |
8 |
0.624 |
0.013 |
0.007 |
90.554 |
| Metro |
10 |
0.630 |
0.007 |
0.004 |
145.183 |
| Metro |
12 |
0.633 |
0.009 |
0.007 |
86.192 |
| Metro |
15 |
0.640 |
0.010 |
0.004 |
145.046 |
| Metro |
18 |
0.623 |
0.010 |
0.010 |
60.712 |
| DEMetro_Z |
5 |
0.338 |
0.013 |
0.005 |
70.131 |
| DEMetro_Z |
8 |
0.512 |
0.013 |
0.007 |
73.928 |
| DEMetro_Z |
10 |
0.623 |
0.007 |
0.004 |
143.702 |
| DEMetro_Z |
12 |
0.629 |
0.009 |
0.007 |
85.652 |
| DEMetro_Z |
15 |
0.621 |
0.010 |
0.004 |
140.684 |
| DEMetro_Z |
18 |
0.620 |
0.010 |
0.010 |
60.369 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
Mode Transitions
Mode Transitions (scatter)
KDE + Init Plots
Forest & Ridge Plots
Pooled
Chain
Pairwise Scatter Plots
Pooled
Chain
Varying_Mode_Distance_with_heavy_Tails
(Mixture,
mm,
12 runs)
Pooled Chains results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
2.067 |
0.052 |
1.036 |
| HMC |
8 |
3.930 |
0.00209 |
6.369 |
| HMC |
10 |
3.733 |
0.00265 |
4.176 |
| HMC |
12 |
3.092 |
0.00909 |
3.770 |
| HMC |
15 |
3.966 |
0.00151 |
3.578 |
| HMC |
18 |
3.033 |
0.0111 |
7.966 |
| SMC |
5 |
4.051 |
0.00123 |
3.475 |
| SMC |
8 |
3.029 |
0.0108 |
5.080 |
| SMC |
10 |
2.026 |
0.067 |
4.931 |
| SMC |
12 |
2.734 |
0.0161 |
2.241 |
| SMC |
15 |
2.930 |
0.00915 |
1.705 |
| SMC |
18 |
3.808 |
0.00254 |
5.614 |
| Metro |
5 |
4.641 |
0.000356 |
3.630 |
| Metro |
8 |
1.723 |
0.112 |
6.534 |
| Metro |
10 |
2.756 |
0.0151 |
2.145 |
| Metro |
12 |
3.458 |
0.00295 |
2.045 |
| Metro |
15 |
2.833 |
0.0101 |
1.355 |
| Metro |
18 |
2.420 |
0.0337 |
7.371 |
| DEMetro_Z |
5 |
4.228 |
0.000732 |
3.071 |
| DEMetro_Z |
8 |
4.321 |
0.00115 |
11.367 |
| DEMetro_Z |
10 |
3.672 |
0.00349 |
8.420 |
| DEMetro_Z |
12 |
2.871 |
0.0143 |
4.593 |
| DEMetro_Z |
15 |
3.378 |
0.00567 |
5.524 |
| DEMetro_Z |
18 |
3.965 |
0.00219 |
20.501 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
-2.881
|
0.0149
|
-0.832
|
| HMC_vs_DEMetro_Z |
1
|
-1.393
|
0.191
|
-0.402
|
| HMC_vs_DEMetro_Z |
2
|
-1.848
|
0.0917
|
-0.533
|
| HMC_vs_DEMetro_Z |
3
|
-0.472
|
0.646
|
-0.136
|
| HMC_vs_DEMetro_Z |
4
|
-1.137
|
0.28
|
-0.328
|
| HMC_vs_DEMetro_Z |
5
|
-1.912
|
0.0822
|
-0.552
|
| Metro_vs_SMC |
0
|
0.169
|
0.869
|
0.049
|
| Metro_vs_SMC |
1
|
0.329
|
0.748
|
0.095
|
| Metro_vs_SMC |
2
|
-1.101
|
0.294
|
-0.318
|
| Metro_vs_SMC |
3
|
-0.186
|
0.856
|
-0.054
|
| Metro_vs_SMC |
4
|
-0.478
|
0.642
|
-0.138
|
| Metro_vs_SMC |
5
|
0.508
|
0.621
|
0.147
|
| Metro_vs_DEMetro_Z |
0
|
0.557
|
0.589
|
0.161
|
| Metro_vs_DEMetro_Z |
1
|
-1.036
|
0.323
|
-0.299
|
| Metro_vs_DEMetro_Z |
2
|
-2.679
|
0.0215
|
-0.773
|
| Metro_vs_DEMetro_Z |
3
|
-1.580
|
0.142
|
-0.456
|
| Metro_vs_DEMetro_Z |
4
|
-2.686
|
0.0212
|
-0.775
|
| Metro_vs_DEMetro_Z |
5
|
-2.130
|
0.0566
|
-0.615
|
| HMC_vs_Metro |
0
|
-3.285
|
0.00727
|
-0.948
|
| HMC_vs_Metro |
1
|
-0.041
|
0.968
|
-0.012
|
| HMC_vs_Metro |
2
|
1.643
|
0.129
|
0.474
|
| HMC_vs_Metro |
3
|
1.365
|
0.199
|
0.394
|
| HMC_vs_Metro |
4
|
2.924
|
0.0138
|
0.844
|
| HMC_vs_Metro |
5
|
0.158
|
0.877
|
0.046
|
| HMC_vs_SMC |
0
|
-2.541
|
0.0275
|
-0.733
|
| HMC_vs_SMC |
1
|
0.591
|
0.566
|
0.171
|
| HMC_vs_SMC |
2
|
-0.275
|
0.788
|
-0.080
|
| HMC_vs_SMC |
3
|
1.031
|
0.325
|
0.298
|
| HMC_vs_SMC |
4
|
1.551
|
0.149
|
0.448
|
| HMC_vs_SMC |
5
|
0.743
|
0.473
|
0.214
|
| DEMetro_Z_vs_SMC |
0
|
-0.383
|
0.709
|
-0.110
|
| DEMetro_Z_vs_SMC |
1
|
1.878
|
0.0871
|
0.542
|
| DEMetro_Z_vs_SMC |
2
|
1.299
|
0.221
|
0.375
|
| DEMetro_Z_vs_SMC |
3
|
1.180
|
0.263
|
0.341
|
| DEMetro_Z_vs_SMC |
4
|
2.236
|
0.047
|
0.645
|
| DEMetro_Z_vs_SMC |
5
|
2.814
|
0.0168
|
0.812
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
0.084 |
0.049 |
0.034 |
1.036 |
| HMC |
8 |
0.239 |
0.059 |
0.028 |
6.369 |
| HMC |
10 |
0.307 |
0.098 |
0.050 |
4.176 |
| HMC |
12 |
0.476 |
0.134 |
0.091 |
3.770 |
| HMC |
15 |
0.804 |
0.153 |
0.182 |
3.578 |
| HMC |
18 |
0.838 |
0.168 |
0.084 |
7.966 |
| SMC |
5 |
0.167 |
0.049 |
0.034 |
3.475 |
| SMC |
8 |
0.203 |
0.059 |
0.028 |
5.080 |
| SMC |
10 |
0.345 |
0.098 |
0.050 |
4.931 |
| SMC |
12 |
0.338 |
0.134 |
0.091 |
2.241 |
| SMC |
15 |
0.463 |
0.153 |
0.182 |
1.705 |
| SMC |
18 |
0.640 |
0.168 |
0.084 |
5.614 |
| Metro |
5 |
0.172 |
0.049 |
0.034 |
3.630 |
| Metro |
8 |
0.244 |
0.059 |
0.028 |
6.534 |
| Metro |
10 |
0.205 |
0.098 |
0.050 |
2.145 |
| Metro |
12 |
0.320 |
0.134 |
0.091 |
2.045 |
| Metro |
15 |
0.400 |
0.153 |
0.182 |
1.355 |
| Metro |
18 |
0.788 |
0.168 |
0.084 |
7.371 |
| DEMetro_Z |
5 |
0.153 |
0.049 |
0.034 |
3.071 |
| DEMetro_Z |
8 |
0.381 |
0.059 |
0.028 |
11.367 |
| DEMetro_Z |
10 |
0.520 |
0.098 |
0.050 |
8.420 |
| DEMetro_Z |
12 |
0.551 |
0.134 |
0.091 |
4.593 |
| DEMetro_Z |
15 |
1.157 |
0.153 |
0.182 |
5.524 |
| DEMetro_Z |
18 |
1.893 |
0.168 |
0.084 |
20.501 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
-1.522 |
0.156 |
-0.440 |
| HMC |
8 |
-0.017 |
0.987 |
-0.009 |
| HMC |
10 |
-1.390 |
0.187 |
-0.426 |
| HMC |
12 |
0.797 |
0.436 |
0.482 |
| HMC |
15 |
-0.617 |
0.547 |
-0.189 |
| HMC |
18 |
1.287 |
0.224 |
3.288 |
| SMC |
5 |
-1.454 |
0.173 |
-0.421 |
| SMC |
8 |
-0.503 |
0.622 |
-0.162 |
| SMC |
10 |
0.021 |
0.983 |
0.007 |
| SMC |
12 |
0.780 |
0.446 |
0.254 |
| SMC |
15 |
-0.614 |
0.549 |
-0.188 |
| SMC |
18 |
0.887 |
0.393 |
2.189 |
| Metro |
5 |
-1.493 |
0.163 |
-0.432 |
| Metro |
8 |
0.483 |
0.637 |
0.452 |
| Metro |
10 |
-1.014 |
0.328 |
-0.311 |
| Metro |
12 |
0.637 |
0.531 |
0.223 |
| Metro |
15 |
-0.604 |
0.556 |
-0.184 |
| Metro |
18 |
0.951 |
0.362 |
2.430 |
| DEMetro_Z |
5 |
-1.454 |
0.174 |
-0.421 |
| DEMetro_Z |
8 |
-1.317 |
0.208 |
-0.413 |
| DEMetro_Z |
10 |
-0.858 |
0.406 |
-0.262 |
| DEMetro_Z |
12 |
0.460 |
0.653 |
0.139 |
| DEMetro_Z |
15 |
-0.593 |
0.563 |
-0.181 |
| DEMetro_Z |
18 |
1.312 |
0.215 |
3.309 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
-1.068
|
0.308
|
-0.308
|
| HMC_vs_SMC |
1
|
0.330
|
0.748
|
0.095
|
| HMC_vs_SMC |
2
|
-3.012
|
0.0118
|
-0.869
|
| HMC_vs_SMC |
3
|
0.413
|
0.688
|
0.119
|
| HMC_vs_SMC |
4
|
-0.470
|
0.647
|
-0.136
|
| HMC_vs_SMC |
5
|
1.241
|
0.24
|
0.358
|
| Metro_vs_DEMetro_Z |
0
|
-0.411
|
0.689
|
-0.119
|
| Metro_vs_DEMetro_Z |
1
|
0.982
|
0.347
|
0.284
|
| Metro_vs_DEMetro_Z |
2
|
-0.993
|
0.342
|
-0.287
|
| Metro_vs_DEMetro_Z |
3
|
0.367
|
0.72
|
0.106
|
| Metro_vs_DEMetro_Z |
4
|
-0.942
|
0.366
|
-0.272
|
| Metro_vs_DEMetro_Z |
5
|
-1.930
|
0.0798
|
-0.557
|
| HMC_vs_Metro |
0
|
-0.344
|
0.737
|
-0.099
|
| HMC_vs_Metro |
1
|
-0.460
|
0.655
|
-0.133
|
| HMC_vs_Metro |
2
|
-2.029
|
0.0674
|
-0.586
|
| HMC_vs_Metro |
3
|
0.511
|
0.619
|
0.148
|
| HMC_vs_Metro |
4
|
-1.915
|
0.0819
|
-0.553
|
| HMC_vs_Metro |
5
|
0.991
|
0.343
|
0.286
|
| HMC_vs_DEMetro_Z |
0
|
-2.422
|
0.0339
|
-0.699
|
| HMC_vs_DEMetro_Z |
1
|
1.070
|
0.308
|
0.309
|
| HMC_vs_DEMetro_Z |
2
|
-2.856
|
0.0156
|
-0.824
|
| HMC_vs_DEMetro_Z |
3
|
0.666
|
0.519
|
0.192
|
| HMC_vs_DEMetro_Z |
4
|
-2.781
|
0.0179
|
-0.803
|
| HMC_vs_DEMetro_Z |
5
|
-0.022
|
0.983
|
-0.006
|
| Metro_vs_SMC |
0
|
-0.338
|
0.741
|
-0.098
|
| Metro_vs_SMC |
1
|
0.669
|
0.517
|
0.193
|
| Metro_vs_SMC |
2
|
-2.017
|
0.0688
|
-0.582
|
| Metro_vs_SMC |
3
|
-0.137
|
0.894
|
-0.039
|
| Metro_vs_SMC |
4
|
1.282
|
0.226
|
0.370
|
| Metro_vs_SMC |
5
|
1.017
|
0.331
|
0.293
|
| DEMetro_Z_vs_SMC |
0
|
0.025
|
0.981
|
0.007
|
| DEMetro_Z_vs_SMC |
1
|
-1.324
|
0.212
|
-0.382
|
| DEMetro_Z_vs_SMC |
2
|
-1.799
|
0.0994
|
-0.519
|
| DEMetro_Z_vs_SMC |
3
|
-0.532
|
0.606
|
-0.153
|
| DEMetro_Z_vs_SMC |
4
|
1.745
|
0.109
|
0.504
|
| DEMetro_Z_vs_SMC |
5
|
2.307
|
0.0415
|
0.666
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
3.355 |
25.768 |
50.962 |
-0.440 |
| HMC |
8 |
7.299 |
7.363 |
7.280 |
-0.009 |
| HMC |
10 |
3.012 |
7.024 |
9.415 |
-0.426 |
| HMC |
12 |
8.712 |
4.533 |
8.662 |
0.482 |
| HMC |
15 |
70.681 |
192.081 |
643.882 |
-0.189 |
| HMC |
18 |
27.558 |
6.741 |
6.332 |
3.288 |
| SMC |
5 |
4.312 |
25.768 |
50.962 |
-0.421 |
| SMC |
8 |
6.187 |
7.363 |
7.280 |
-0.162 |
| SMC |
10 |
7.087 |
7.024 |
9.415 |
0.007 |
| SMC |
12 |
6.736 |
4.533 |
8.662 |
0.254 |
| SMC |
15 |
71.352 |
192.081 |
643.882 |
-0.188 |
| SMC |
18 |
20.602 |
6.741 |
6.332 |
2.189 |
| Metro |
5 |
3.764 |
25.768 |
50.962 |
-0.432 |
| Metro |
8 |
10.653 |
7.363 |
7.280 |
0.452 |
| Metro |
10 |
4.093 |
7.024 |
9.415 |
-0.311 |
| Metro |
12 |
6.462 |
4.533 |
8.662 |
0.223 |
| Metro |
15 |
73.306 |
192.081 |
643.882 |
-0.184 |
| Metro |
18 |
22.126 |
6.741 |
6.332 |
2.430 |
| DEMetro_Z |
5 |
4.334 |
25.768 |
50.962 |
-0.421 |
| DEMetro_Z |
8 |
4.353 |
7.363 |
7.280 |
-0.413 |
| DEMetro_Z |
10 |
4.559 |
7.024 |
9.415 |
-0.262 |
| DEMetro_Z |
12 |
5.734 |
4.533 |
8.662 |
0.139 |
| DEMetro_Z |
15 |
75.368 |
192.081 |
643.882 |
-0.181 |
| DEMetro_Z |
18 |
27.696 |
6.741 |
6.332 |
3.309 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
1.369 |
0.185 |
0.511 |
| HMC |
8 |
4.510 |
0.000766 |
7.581 |
| HMC |
10 |
4.437 |
0.000852 |
7.036 |
| HMC |
12 |
3.961 |
0.00192 |
5.721 |
| HMC |
15 |
4.058 |
0.00116 |
3.304 |
| HMC |
18 |
3.335 |
0.00652 |
10.927 |
| SMC |
5 |
4.908 |
0.00014 |
3.030 |
| SMC |
8 |
7.911 |
5.11e-06 |
13.566 |
| SMC |
10 |
4.777 |
0.000546 |
14.653 |
| SMC |
12 |
5.302 |
0.000165 |
6.093 |
| SMC |
15 |
4.764 |
0.000159 |
2.703 |
| SMC |
18 |
7.002 |
1.55e-05 |
10.668 |
| Metro |
5 |
3.714 |
0.00125 |
1.660 |
| Metro |
8 |
1.936 |
0.0788 |
8.872 |
| Metro |
10 |
4.403 |
0.000766 |
4.851 |
| Metro |
12 |
4.840 |
0.000207 |
3.420 |
| Metro |
15 |
3.446 |
0.00263 |
1.758 |
| Metro |
18 |
2.715 |
0.0199 |
10.418 |
| DEMetro_Z |
5 |
4.913 |
7e-05 |
1.856 |
| DEMetro_Z |
8 |
5.159 |
0.000288 |
13.035 |
| DEMetro_Z |
10 |
5.272 |
0.000247 |
15.274 |
| DEMetro_Z |
12 |
4.055 |
0.00175 |
8.146 |
| DEMetro_Z |
15 |
3.693 |
0.0031 |
5.234 |
| DEMetro_Z |
18 |
4.377 |
0.00109 |
26.524 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
-0.478
|
0.642
|
-0.138
|
| Metro_vs_DEMetro_Z |
1
|
-0.811
|
0.435
|
-0.234
|
| Metro_vs_DEMetro_Z |
2
|
-3.452
|
0.0054
|
-0.997
|
| Metro_vs_DEMetro_Z |
3
|
-2.409
|
0.0347
|
-0.695
|
| Metro_vs_DEMetro_Z |
4
|
-2.696
|
0.0208
|
-0.778
|
| Metro_vs_DEMetro_Z |
5
|
-2.118
|
0.0578
|
-0.611
|
| DEMetro_Z_vs_SMC |
0
|
-1.924
|
0.0806
|
-0.555
|
| DEMetro_Z_vs_SMC |
1
|
-0.171
|
0.868
|
-0.049
|
| DEMetro_Z_vs_SMC |
2
|
0.197
|
0.847
|
0.057
|
| DEMetro_Z_vs_SMC |
3
|
0.744
|
0.472
|
0.215
|
| DEMetro_Z_vs_SMC |
4
|
1.752
|
0.108
|
0.506
|
| DEMetro_Z_vs_SMC |
5
|
2.665
|
0.022
|
0.769
|
| HMC_vs_DEMetro_Z |
0
|
-4.168
|
0.00157
|
-1.203
|
| HMC_vs_DEMetro_Z |
1
|
-1.681
|
0.121
|
-0.485
|
| HMC_vs_DEMetro_Z |
2
|
-2.729
|
0.0196
|
-0.788
|
| HMC_vs_DEMetro_Z |
3
|
-1.173
|
0.265
|
-0.339
|
| HMC_vs_DEMetro_Z |
4
|
-1.297
|
0.221
|
-0.374
|
| HMC_vs_DEMetro_Z |
5
|
-1.988
|
0.0723
|
-0.574
|
| HMC_vs_Metro |
0
|
-2.526
|
0.0282
|
-0.729
|
| HMC_vs_Metro |
1
|
-0.274
|
0.789
|
-0.079
|
| HMC_vs_Metro |
2
|
1.080
|
0.303
|
0.312
|
| HMC_vs_Metro |
3
|
1.596
|
0.139
|
0.461
|
| HMC_vs_Metro |
4
|
2.680
|
0.0214
|
0.774
|
| HMC_vs_Metro |
5
|
0.107
|
0.917
|
0.031
|
| HMC_vs_SMC |
0
|
-4.528
|
0.00086
|
-1.307
|
| HMC_vs_SMC |
1
|
-2.806
|
0.0171
|
-0.810
|
| HMC_vs_SMC |
2
|
-2.233
|
0.0473
|
-0.645
|
| HMC_vs_SMC |
3
|
-0.174
|
0.865
|
-0.050
|
| HMC_vs_SMC |
4
|
0.579
|
0.574
|
0.167
|
| HMC_vs_SMC |
5
|
0.069
|
0.946
|
0.020
|
| Metro_vs_SMC |
0
|
-2.734
|
0.0194
|
-0.789
|
| Metro_vs_SMC |
1
|
-0.844
|
0.416
|
-0.244
|
| Metro_vs_SMC |
2
|
-2.779
|
0.018
|
-0.802
|
| Metro_vs_SMC |
3
|
-1.747
|
0.109
|
-0.504
|
| Metro_vs_SMC |
4
|
-1.512
|
0.159
|
-0.436
|
| Metro_vs_SMC |
5
|
-0.059
|
0.954
|
-0.017
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
0.178 |
0.141 |
0.074 |
0.511 |
| HMC |
8 |
0.324 |
0.136 |
0.025 |
7.581 |
| HMC |
10 |
0.358 |
0.150 |
0.030 |
7.036 |
| HMC |
12 |
0.560 |
0.181 |
0.066 |
5.721 |
| HMC |
15 |
0.838 |
0.224 |
0.186 |
3.304 |
| HMC |
18 |
0.875 |
0.224 |
0.060 |
10.927 |
| SMC |
5 |
0.364 |
0.141 |
0.074 |
3.030 |
| SMC |
8 |
0.472 |
0.136 |
0.025 |
13.566 |
| SMC |
10 |
0.584 |
0.150 |
0.030 |
14.653 |
| SMC |
12 |
0.585 |
0.181 |
0.066 |
6.093 |
| SMC |
15 |
0.726 |
0.224 |
0.186 |
2.703 |
| SMC |
18 |
0.859 |
0.224 |
0.060 |
10.668 |
| Metro |
5 |
0.263 |
0.141 |
0.074 |
1.660 |
| Metro |
8 |
0.356 |
0.136 |
0.025 |
8.872 |
| Metro |
10 |
0.293 |
0.150 |
0.030 |
4.851 |
| Metro |
12 |
0.408 |
0.181 |
0.066 |
3.420 |
| Metro |
15 |
0.550 |
0.224 |
0.186 |
1.758 |
| Metro |
18 |
0.845 |
0.224 |
0.060 |
10.418 |
| DEMetro_Z |
5 |
0.277 |
0.141 |
0.074 |
1.856 |
| DEMetro_Z |
8 |
0.459 |
0.136 |
0.025 |
13.035 |
| DEMetro_Z |
10 |
0.602 |
0.150 |
0.030 |
15.274 |
| DEMetro_Z |
12 |
0.721 |
0.181 |
0.066 |
8.146 |
| DEMetro_Z |
15 |
1.196 |
0.224 |
0.186 |
5.234 |
| DEMetro_Z |
18 |
1.804 |
0.224 |
0.060 |
26.524 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
3.163 |
0.00689 |
2.594 |
| HMC |
8 |
3.949 |
0.00212 |
8.399 |
| HMC |
10 |
4.123 |
0.00154 |
7.817 |
| HMC |
12 |
3.652 |
0.00329 |
4.889 |
| HMC |
15 |
4.495 |
0.000885 |
17.804 |
| HMC |
18 |
3.067 |
0.0105 |
10.375 |
| SMC |
5 |
7.755 |
3.57e-06 |
8.259 |
| SMC |
8 |
6.343 |
4.27e-05 |
10.966 |
| SMC |
10 |
2.866 |
0.0152 |
11.220 |
| SMC |
12 |
3.779 |
0.00215 |
3.366 |
| SMC |
15 |
4.310 |
0.00115 |
10.063 |
| SMC |
18 |
4.277 |
0.00118 |
8.166 |
| Metro |
5 |
4.397 |
0.00057 |
3.432 |
| Metro |
8 |
3.513 |
0.00391 |
3.705 |
| Metro |
10 |
2.964 |
0.0118 |
4.046 |
| Metro |
12 |
2.533 |
0.0224 |
1.709 |
| Metro |
15 |
4.175 |
0.00137 |
7.089 |
| Metro |
18 |
2.615 |
0.0239 |
10.580 |
| DEMetro_Z |
5 |
5.826 |
5.05e-05 |
5.213 |
| DEMetro_Z |
8 |
4.681 |
0.00064 |
14.336 |
| DEMetro_Z |
10 |
4.182 |
0.0015 |
16.223 |
| DEMetro_Z |
12 |
3.217 |
0.00782 |
6.665 |
| DEMetro_Z |
15 |
3.432 |
0.00558 |
28.862 |
| DEMetro_Z |
18 |
3.907 |
0.00244 |
30.089 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
-2.155
|
0.0542
|
-0.622
|
| DEMetro_Z_vs_SMC |
1
|
0.957
|
0.359
|
0.276
|
| DEMetro_Z_vs_SMC |
2
|
1.080
|
0.303
|
0.312
|
| DEMetro_Z_vs_SMC |
3
|
1.277
|
0.228
|
0.369
|
| DEMetro_Z_vs_SMC |
4
|
2.140
|
0.0556
|
0.618
|
| DEMetro_Z_vs_SMC |
5
|
2.837
|
0.0162
|
0.819
|
| HMC_vs_Metro |
0
|
-0.668
|
0.518
|
-0.193
|
| HMC_vs_Metro |
1
|
2.318
|
0.0407
|
0.669
|
| HMC_vs_Metro |
2
|
1.515
|
0.158
|
0.437
|
| HMC_vs_Metro |
3
|
2.041
|
0.0659
|
0.589
|
| HMC_vs_Metro |
4
|
3.280
|
0.00733
|
0.947
|
| HMC_vs_Metro |
5
|
-0.041
|
0.968
|
-0.012
|
| Metro_vs_DEMetro_Z |
0
|
-1.583
|
0.142
|
-0.457
|
| Metro_vs_DEMetro_Z |
1
|
-3.330
|
0.00671
|
-0.961
|
| Metro_vs_DEMetro_Z |
2
|
-3.112
|
0.0099
|
-0.898
|
| Metro_vs_DEMetro_Z |
3
|
-2.231
|
0.0475
|
-0.644
|
| Metro_vs_DEMetro_Z |
4
|
-2.842
|
0.016
|
-0.820
|
| Metro_vs_DEMetro_Z |
5
|
-2.157
|
0.054
|
-0.623
|
| HMC_vs_SMC |
0
|
-4.182
|
0.00153
|
-1.207
|
| HMC_vs_SMC |
1
|
-0.952
|
0.362
|
-0.275
|
| HMC_vs_SMC |
2
|
-0.760
|
0.463
|
-0.219
|
| HMC_vs_SMC |
3
|
0.868
|
0.404
|
0.251
|
| HMC_vs_SMC |
4
|
1.422
|
0.183
|
0.410
|
| HMC_vs_SMC |
5
|
0.521
|
0.612
|
0.151
|
| Metro_vs_SMC |
0
|
-4.054
|
0.0019
|
-1.170
|
| Metro_vs_SMC |
1
|
-3.494
|
0.00503
|
-1.009
|
| Metro_vs_SMC |
2
|
-1.644
|
0.128
|
-0.475
|
| Metro_vs_SMC |
3
|
-1.387
|
0.193
|
-0.400
|
| Metro_vs_SMC |
4
|
-0.921
|
0.377
|
-0.266
|
| Metro_vs_SMC |
5
|
0.521
|
0.612
|
0.150
|
| HMC_vs_DEMetro_Z |
0
|
-2.096
|
0.06
|
-0.605
|
| HMC_vs_DEMetro_Z |
1
|
-1.415
|
0.185
|
-0.408
|
| HMC_vs_DEMetro_Z |
2
|
-2.167
|
0.053
|
-0.626
|
| HMC_vs_DEMetro_Z |
3
|
-0.838
|
0.42
|
-0.242
|
| HMC_vs_DEMetro_Z |
4
|
-1.249
|
0.237
|
-0.361
|
| HMC_vs_DEMetro_Z |
5
|
-2.123
|
0.0573
|
-0.613
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
0.025 |
0.012 |
0.005 |
2.594 |
| HMC |
8 |
0.041 |
0.010 |
0.004 |
8.399 |
| HMC |
10 |
0.045 |
0.011 |
0.004 |
7.817 |
| HMC |
12 |
0.064 |
0.015 |
0.010 |
4.889 |
| HMC |
15 |
0.085 |
0.010 |
0.004 |
17.804 |
| HMC |
18 |
0.074 |
0.013 |
0.006 |
10.375 |
| SMC |
5 |
0.054 |
0.012 |
0.005 |
8.259 |
| SMC |
8 |
0.051 |
0.010 |
0.004 |
10.966 |
| SMC |
10 |
0.059 |
0.011 |
0.004 |
11.220 |
| SMC |
12 |
0.049 |
0.015 |
0.010 |
3.366 |
| SMC |
15 |
0.052 |
0.010 |
0.004 |
10.063 |
| SMC |
18 |
0.061 |
0.013 |
0.006 |
8.166 |
| Metro |
5 |
0.029 |
0.012 |
0.005 |
3.432 |
| Metro |
8 |
0.024 |
0.010 |
0.004 |
3.705 |
| Metro |
10 |
0.029 |
0.011 |
0.004 |
4.046 |
| Metro |
12 |
0.033 |
0.015 |
0.010 |
1.709 |
| Metro |
15 |
0.040 |
0.010 |
0.004 |
7.089 |
| Metro |
18 |
0.075 |
0.013 |
0.006 |
10.580 |
| DEMetro_Z |
5 |
0.039 |
0.012 |
0.005 |
5.213 |
| DEMetro_Z |
8 |
0.063 |
0.010 |
0.004 |
14.336 |
| DEMetro_Z |
10 |
0.081 |
0.011 |
0.004 |
16.223 |
| DEMetro_Z |
12 |
0.082 |
0.015 |
0.010 |
6.665 |
| DEMetro_Z |
15 |
0.131 |
0.010 |
0.004 |
28.862 |
| DEMetro_Z |
18 |
0.190 |
0.013 |
0.006 |
30.089 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
R Hat (scatter)
Mode Transitions
One Chain results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
2.285 |
0.0338 |
1.182 |
| HMC |
8 |
2.859 |
0.0145 |
4.200 |
| HMC |
10 |
4.649 |
0.000528 |
5.702 |
| HMC |
12 |
2.308 |
0.039 |
2.719 |
| HMC |
15 |
2.032 |
0.0635 |
2.166 |
| HMC |
18 |
3.520 |
0.00463 |
9.205 |
| SMC |
5 |
2.968 |
0.00939 |
2.071 |
| SMC |
8 |
4.010 |
0.00184 |
6.956 |
| SMC |
10 |
3.543 |
0.00352 |
3.368 |
| SMC |
12 |
2.397 |
0.035 |
6.554 |
| SMC |
15 |
3.177 |
0.00774 |
3.852 |
| SMC |
18 |
3.242 |
0.00734 |
5.636 |
| Metro |
5 |
3.735 |
0.00241 |
3.501 |
| Metro |
8 |
2.725 |
0.0194 |
7.479 |
| Metro |
10 |
3.417 |
0.00444 |
3.172 |
| Metro |
12 |
2.106 |
0.051 |
1.332 |
| Metro |
15 |
2.690 |
0.0135 |
1.187 |
| Metro |
18 |
3.507 |
0.00472 |
8.674 |
| DEMetro_Z |
5 |
4.148 |
0.00113 |
4.065 |
| DEMetro_Z |
8 |
4.227 |
0.00114 |
5.425 |
| DEMetro_Z |
10 |
2.102 |
0.0583 |
3.997 |
| DEMetro_Z |
12 |
3.484 |
0.00386 |
3.166 |
| DEMetro_Z |
15 |
2.611 |
0.0236 |
5.496 |
| DEMetro_Z |
18 |
3.148 |
0.0092 |
16.606 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
-2.781
|
0.0179
|
-0.803
|
| HMC_vs_DEMetro_Z |
1
|
-0.669
|
0.517
|
-0.193
|
| HMC_vs_DEMetro_Z |
2
|
0.779
|
0.452
|
0.225
|
| HMC_vs_DEMetro_Z |
3
|
-0.280
|
0.785
|
-0.081
|
| HMC_vs_DEMetro_Z |
4
|
-1.239
|
0.241
|
-0.358
|
| HMC_vs_DEMetro_Z |
5
|
-1.148
|
0.275
|
-0.331
|
| Metro_vs_SMC |
0
|
1.150
|
0.274
|
0.332
|
| Metro_vs_SMC |
1
|
0.137
|
0.893
|
0.040
|
| Metro_vs_SMC |
2
|
-0.121
|
0.906
|
-0.035
|
| Metro_vs_SMC |
3
|
-1.785
|
0.102
|
-0.515
|
| Metro_vs_SMC |
4
|
-1.978
|
0.0735
|
-0.571
|
| Metro_vs_SMC |
5
|
1.176
|
0.264
|
0.340
|
| Metro_vs_DEMetro_Z |
0
|
-0.420
|
0.683
|
-0.121
|
| Metro_vs_DEMetro_Z |
1
|
0.939
|
0.368
|
0.271
|
| Metro_vs_DEMetro_Z |
2
|
-0.343
|
0.738
|
-0.099
|
| Metro_vs_DEMetro_Z |
3
|
-1.649
|
0.127
|
-0.476
|
| Metro_vs_DEMetro_Z |
4
|
-2.017
|
0.0687
|
-0.582
|
| Metro_vs_DEMetro_Z |
5
|
-1.354
|
0.203
|
-0.391
|
| HMC_vs_Metro |
0
|
-2.078
|
0.0619
|
-0.600
|
| HMC_vs_Metro |
1
|
-1.230
|
0.244
|
-0.355
|
| HMC_vs_Metro |
2
|
1.483
|
0.166
|
0.428
|
| HMC_vs_Metro |
3
|
1.018
|
0.33
|
0.294
|
| HMC_vs_Metro |
4
|
0.831
|
0.423
|
0.240
|
| HMC_vs_Metro |
5
|
0.156
|
0.879
|
0.045
|
| HMC_vs_SMC |
0
|
-1.150
|
0.274
|
-0.332
|
| HMC_vs_SMC |
1
|
-1.158
|
0.271
|
-0.334
|
| HMC_vs_SMC |
2
|
1.639
|
0.129
|
0.473
|
| HMC_vs_SMC |
3
|
-1.648
|
0.128
|
-0.476
|
| HMC_vs_SMC |
4
|
-1.479
|
0.167
|
-0.427
|
| HMC_vs_SMC |
5
|
1.069
|
0.308
|
0.309
|
| DEMetro_Z_vs_SMC |
0
|
1.818
|
0.0964
|
0.525
|
| DEMetro_Z_vs_SMC |
1
|
-0.693
|
0.503
|
-0.200
|
| DEMetro_Z_vs_SMC |
2
|
0.440
|
0.668
|
0.127
|
| DEMetro_Z_vs_SMC |
3
|
-1.323
|
0.213
|
-0.382
|
| DEMetro_Z_vs_SMC |
4
|
0.760
|
0.463
|
0.219
|
| DEMetro_Z_vs_SMC |
5
|
2.008
|
0.0699
|
0.580
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
0.089 |
0.049 |
0.034 |
1.182 |
| HMC |
8 |
0.178 |
0.059 |
0.028 |
4.200 |
| HMC |
10 |
0.383 |
0.098 |
0.050 |
5.702 |
| HMC |
12 |
0.381 |
0.134 |
0.091 |
2.719 |
| HMC |
15 |
0.547 |
0.153 |
0.182 |
2.166 |
| HMC |
18 |
0.942 |
0.168 |
0.084 |
9.205 |
| SMC |
5 |
0.119 |
0.049 |
0.034 |
2.071 |
| SMC |
8 |
0.256 |
0.059 |
0.028 |
6.956 |
| SMC |
10 |
0.267 |
0.098 |
0.050 |
3.368 |
| SMC |
12 |
0.729 |
0.134 |
0.091 |
6.554 |
| SMC |
15 |
0.853 |
0.153 |
0.182 |
3.852 |
| SMC |
18 |
0.642 |
0.168 |
0.084 |
5.636 |
| Metro |
5 |
0.168 |
0.049 |
0.034 |
3.501 |
| Metro |
8 |
0.271 |
0.059 |
0.028 |
7.479 |
| Metro |
10 |
0.257 |
0.098 |
0.050 |
3.172 |
| Metro |
12 |
0.255 |
0.134 |
0.091 |
1.332 |
| Metro |
15 |
0.369 |
0.153 |
0.182 |
1.187 |
| Metro |
18 |
0.898 |
0.168 |
0.084 |
8.674 |
| DEMetro_Z |
5 |
0.187 |
0.049 |
0.034 |
4.065 |
| DEMetro_Z |
8 |
0.213 |
0.059 |
0.028 |
5.425 |
| DEMetro_Z |
10 |
0.298 |
0.098 |
0.050 |
3.997 |
| DEMetro_Z |
12 |
0.422 |
0.134 |
0.091 |
3.166 |
| DEMetro_Z |
15 |
1.152 |
0.153 |
0.182 |
5.496 |
| DEMetro_Z |
18 |
1.565 |
0.168 |
0.084 |
16.606 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
-1.584 |
0.141 |
-0.458 |
| HMC |
8 |
-0.142 |
0.888 |
-0.080 |
| HMC |
10 |
-1.066 |
0.306 |
-0.321 |
| HMC |
12 |
-0.272 |
0.789 |
-0.083 |
| HMC |
15 |
-0.600 |
0.558 |
-0.183 |
| HMC |
18 |
1.000 |
0.338 |
2.558 |
| SMC |
5 |
-1.527 |
0.155 |
-0.441 |
| SMC |
8 |
-1.698 |
0.114 |
-0.507 |
| SMC |
10 |
-1.221 |
0.242 |
-0.379 |
| SMC |
12 |
0.321 |
0.752 |
0.101 |
| SMC |
15 |
-0.612 |
0.55 |
-0.187 |
| SMC |
18 |
0.873 |
0.401 |
2.216 |
| Metro |
5 |
-1.505 |
0.16 |
-0.435 |
| Metro |
8 |
0.384 |
0.707 |
0.353 |
| Metro |
10 |
-1.117 |
0.284 |
-0.338 |
| Metro |
12 |
-0.201 |
0.844 |
-0.061 |
| Metro |
15 |
-0.598 |
0.559 |
-0.183 |
| Metro |
18 |
1.325 |
0.212 |
3.475 |
| DEMetro_Z |
5 |
-1.545 |
0.151 |
-0.446 |
| DEMetro_Z |
8 |
-1.686 |
0.113 |
-0.527 |
| DEMetro_Z |
10 |
-0.853 |
0.408 |
-0.264 |
| DEMetro_Z |
12 |
0.069 |
0.946 |
0.021 |
| DEMetro_Z |
15 |
-0.601 |
0.557 |
-0.184 |
| DEMetro_Z |
18 |
1.184 |
0.261 |
3.066 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
-1.113
|
0.289
|
-0.321
|
| HMC_vs_SMC |
1
|
0.935
|
0.37
|
0.270
|
| HMC_vs_SMC |
2
|
0.763
|
0.462
|
0.220
|
| HMC_vs_SMC |
3
|
-1.214
|
0.25
|
-0.351
|
| HMC_vs_SMC |
4
|
0.951
|
0.362
|
0.275
|
| HMC_vs_SMC |
5
|
0.978
|
0.349
|
0.282
|
| Metro_vs_DEMetro_Z |
0
|
1.462
|
0.172
|
0.422
|
| Metro_vs_DEMetro_Z |
1
|
1.023
|
0.328
|
0.295
|
| Metro_vs_DEMetro_Z |
2
|
-1.824
|
0.0953
|
-0.527
|
| Metro_vs_DEMetro_Z |
3
|
-1.802
|
0.0991
|
-0.520
|
| Metro_vs_DEMetro_Z |
4
|
0.213
|
0.835
|
0.062
|
| Metro_vs_DEMetro_Z |
5
|
0.382
|
0.71
|
0.110
|
| HMC_vs_Metro |
0
|
-2.117
|
0.0578
|
-0.611
|
| HMC_vs_Metro |
1
|
-0.419
|
0.684
|
-0.121
|
| HMC_vs_Metro |
2
|
0.267
|
0.794
|
0.077
|
| HMC_vs_Metro |
3
|
-0.291
|
0.777
|
-0.084
|
| HMC_vs_Metro |
4
|
-0.092
|
0.929
|
-0.026
|
| HMC_vs_Metro |
5
|
-0.908
|
0.383
|
-0.262
|
| HMC_vs_DEMetro_Z |
0
|
-0.883
|
0.396
|
-0.255
|
| HMC_vs_DEMetro_Z |
1
|
0.922
|
0.376
|
0.266
|
| HMC_vs_DEMetro_Z |
2
|
-0.741
|
0.474
|
-0.214
|
| HMC_vs_DEMetro_Z |
3
|
-1.336
|
0.208
|
-0.386
|
| HMC_vs_DEMetro_Z |
4
|
0.097
|
0.924
|
0.028
|
| HMC_vs_DEMetro_Z |
5
|
-0.875
|
0.4
|
-0.253
|
| Metro_vs_SMC |
0
|
0.420
|
0.683
|
0.121
|
| Metro_vs_SMC |
1
|
0.971
|
0.353
|
0.280
|
| Metro_vs_SMC |
2
|
0.691
|
0.504
|
0.200
|
| Metro_vs_SMC |
3
|
-1.084
|
0.301
|
-0.313
|
| Metro_vs_SMC |
4
|
0.881
|
0.397
|
0.254
|
| Metro_vs_SMC |
5
|
1.369
|
0.198
|
0.395
|
| DEMetro_Z_vs_SMC |
0
|
-0.241
|
0.814
|
-0.070
|
| DEMetro_Z_vs_SMC |
1
|
-0.180
|
0.861
|
-0.052
|
| DEMetro_Z_vs_SMC |
2
|
1.628
|
0.132
|
0.470
|
| DEMetro_Z_vs_SMC |
3
|
-0.482
|
0.64
|
-0.139
|
| DEMetro_Z_vs_SMC |
4
|
1.425
|
0.182
|
0.411
|
| DEMetro_Z_vs_SMC |
5
|
1.956
|
0.0764
|
0.565
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
2.451 |
25.768 |
50.962 |
-0.458 |
| HMC |
8 |
6.781 |
7.363 |
7.280 |
-0.080 |
| HMC |
10 |
3.999 |
7.024 |
9.415 |
-0.321 |
| HMC |
12 |
3.817 |
4.533 |
8.662 |
-0.083 |
| HMC |
15 |
74.092 |
192.081 |
643.882 |
-0.183 |
| HMC |
18 |
22.938 |
6.741 |
6.332 |
2.558 |
| SMC |
5 |
3.271 |
25.768 |
50.962 |
-0.441 |
| SMC |
8 |
3.670 |
7.363 |
7.280 |
-0.507 |
| SMC |
10 |
3.458 |
7.024 |
9.415 |
-0.379 |
| SMC |
12 |
5.408 |
4.533 |
8.662 |
0.101 |
| SMC |
15 |
71.698 |
192.081 |
643.882 |
-0.187 |
| SMC |
18 |
20.773 |
6.741 |
6.332 |
2.216 |
| Metro |
5 |
3.622 |
25.768 |
50.962 |
-0.435 |
| Metro |
8 |
9.933 |
7.363 |
7.280 |
0.353 |
| Metro |
10 |
3.843 |
7.024 |
9.415 |
-0.338 |
| Metro |
12 |
4.003 |
4.533 |
8.662 |
-0.061 |
| Metro |
15 |
74.451 |
192.081 |
643.882 |
-0.183 |
| Metro |
18 |
28.742 |
6.741 |
6.332 |
3.475 |
| DEMetro_Z |
5 |
3.025 |
25.768 |
50.962 |
-0.446 |
| DEMetro_Z |
8 |
3.525 |
7.363 |
7.280 |
-0.527 |
| DEMetro_Z |
10 |
4.542 |
7.024 |
9.415 |
-0.264 |
| DEMetro_Z |
12 |
4.718 |
4.533 |
8.662 |
0.021 |
| DEMetro_Z |
15 |
73.823 |
192.081 |
643.882 |
-0.184 |
| DEMetro_Z |
18 |
26.155 |
6.741 |
6.332 |
3.066 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
0.900 |
0.38 |
0.301 |
| HMC |
8 |
3.940 |
0.00195 |
5.352 |
| HMC |
10 |
5.575 |
0.000135 |
9.459 |
| HMC |
12 |
2.663 |
0.0209 |
4.016 |
| HMC |
15 |
2.219 |
0.0444 |
2.074 |
| HMC |
18 |
3.877 |
0.00251 |
12.927 |
| SMC |
5 |
2.229 |
0.037 |
1.042 |
| SMC |
8 |
5.401 |
0.000181 |
9.739 |
| SMC |
10 |
5.142 |
0.000238 |
6.814 |
| SMC |
12 |
3.180 |
0.00859 |
9.923 |
| SMC |
15 |
3.399 |
0.00481 |
3.489 |
| SMC |
18 |
4.524 |
0.000776 |
8.810 |
| Metro |
5 |
3.229 |
0.00407 |
1.522 |
| Metro |
8 |
2.827 |
0.0162 |
8.217 |
| Metro |
10 |
5.264 |
0.000185 |
6.490 |
| Metro |
12 |
2.920 |
0.0113 |
2.464 |
| Metro |
15 |
3.412 |
0.0025 |
1.408 |
| Metro |
18 |
3.546 |
0.00449 |
12.392 |
| DEMetro_Z |
5 |
4.340 |
0.000281 |
1.965 |
| DEMetro_Z |
8 |
5.313 |
0.000171 |
6.575 |
| DEMetro_Z |
10 |
3.367 |
0.00605 |
8.307 |
| DEMetro_Z |
12 |
5.410 |
0.000115 |
5.220 |
| DEMetro_Z |
15 |
2.901 |
0.0136 |
4.837 |
| DEMetro_Z |
18 |
3.313 |
0.00688 |
21.874 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
-0.893
|
0.391
|
-0.258
|
| Metro_vs_DEMetro_Z |
1
|
0.767
|
0.459
|
0.221
|
| Metro_vs_DEMetro_Z |
2
|
-0.588
|
0.569
|
-0.170
|
| Metro_vs_DEMetro_Z |
3
|
-2.132
|
0.0564
|
-0.615
|
| Metro_vs_DEMetro_Z |
4
|
-2.089
|
0.0607
|
-0.603
|
| Metro_vs_DEMetro_Z |
5
|
-1.277
|
0.228
|
-0.369
|
| DEMetro_Z_vs_SMC |
0
|
2.572
|
0.0259
|
0.743
|
| DEMetro_Z_vs_SMC |
1
|
-1.186
|
0.26
|
-0.342
|
| DEMetro_Z_vs_SMC |
2
|
0.702
|
0.498
|
0.203
|
| DEMetro_Z_vs_SMC |
3
|
-1.638
|
0.13
|
-0.473
|
| DEMetro_Z_vs_SMC |
4
|
0.814
|
0.433
|
0.235
|
| DEMetro_Z_vs_SMC |
5
|
1.937
|
0.0788
|
0.559
|
| HMC_vs_DEMetro_Z |
0
|
-3.846
|
0.00272
|
-1.110
|
| HMC_vs_DEMetro_Z |
1
|
-0.724
|
0.484
|
-0.209
|
| HMC_vs_DEMetro_Z |
2
|
0.375
|
0.715
|
0.108
|
| HMC_vs_DEMetro_Z |
3
|
-0.641
|
0.534
|
-0.185
|
| HMC_vs_DEMetro_Z |
4
|
-1.283
|
0.226
|
-0.370
|
| HMC_vs_DEMetro_Z |
5
|
-1.117
|
0.288
|
-0.322
|
| HMC_vs_Metro |
0
|
-2.822
|
0.0166
|
-0.815
|
| HMC_vs_Metro |
1
|
-0.995
|
0.341
|
-0.287
|
| HMC_vs_Metro |
2
|
1.316
|
0.215
|
0.380
|
| HMC_vs_Metro |
3
|
0.828
|
0.425
|
0.239
|
| HMC_vs_Metro |
4
|
0.648
|
0.53
|
0.187
|
| HMC_vs_Metro |
5
|
0.125
|
0.903
|
0.036
|
| HMC_vs_SMC |
0
|
-1.627
|
0.132
|
-0.470
|
| HMC_vs_SMC |
1
|
-1.851
|
0.0912
|
-0.534
|
| HMC_vs_SMC |
2
|
1.472
|
0.169
|
0.425
|
| HMC_vs_SMC |
3
|
-2.188
|
0.0511
|
-0.632
|
| HMC_vs_SMC |
4
|
-1.446
|
0.176
|
-0.417
|
| HMC_vs_SMC |
5
|
0.960
|
0.358
|
0.277
|
| Metro_vs_SMC |
0
|
0.838
|
0.42
|
0.242
|
| Metro_vs_SMC |
1
|
-0.367
|
0.72
|
-0.106
|
| Metro_vs_SMC |
2
|
-0.140
|
0.891
|
-0.041
|
| Metro_vs_SMC |
3
|
-2.196
|
0.0505
|
-0.634
|
| Metro_vs_SMC |
4
|
-1.893
|
0.085
|
-0.546
|
| Metro_vs_SMC |
5
|
1.068
|
0.308
|
0.308
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
0.163 |
0.141 |
0.074 |
0.301 |
| HMC |
8 |
0.268 |
0.136 |
0.025 |
5.352 |
| HMC |
10 |
0.430 |
0.150 |
0.030 |
9.459 |
| HMC |
12 |
0.447 |
0.181 |
0.066 |
4.016 |
| HMC |
15 |
0.609 |
0.224 |
0.186 |
2.074 |
| HMC |
18 |
0.994 |
0.224 |
0.060 |
12.927 |
| SMC |
5 |
0.217 |
0.141 |
0.074 |
1.042 |
| SMC |
8 |
0.377 |
0.136 |
0.025 |
9.739 |
| SMC |
10 |
0.352 |
0.150 |
0.030 |
6.814 |
| SMC |
12 |
0.839 |
0.181 |
0.066 |
9.923 |
| SMC |
15 |
0.872 |
0.224 |
0.186 |
3.489 |
| SMC |
18 |
0.749 |
0.224 |
0.060 |
8.810 |
| Metro |
5 |
0.253 |
0.141 |
0.074 |
1.522 |
| Metro |
8 |
0.340 |
0.136 |
0.025 |
8.217 |
| Metro |
10 |
0.342 |
0.150 |
0.030 |
6.490 |
| Metro |
12 |
0.344 |
0.181 |
0.066 |
2.464 |
| Metro |
15 |
0.485 |
0.224 |
0.186 |
1.408 |
| Metro |
18 |
0.962 |
0.224 |
0.060 |
12.392 |
| DEMetro_Z |
5 |
0.285 |
0.141 |
0.074 |
1.965 |
| DEMetro_Z |
8 |
0.299 |
0.136 |
0.025 |
6.575 |
| DEMetro_Z |
10 |
0.396 |
0.150 |
0.030 |
8.307 |
| DEMetro_Z |
12 |
0.527 |
0.181 |
0.066 |
5.220 |
| DEMetro_Z |
15 |
1.123 |
0.224 |
0.186 |
4.837 |
| DEMetro_Z |
18 |
1.527 |
0.224 |
0.060 |
21.874 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
2.538 |
0.0216 |
1.608 |
| HMC |
8 |
2.922 |
0.0134 |
6.220 |
| HMC |
10 |
5.157 |
0.000276 |
10.434 |
| HMC |
12 |
2.333 |
0.0379 |
3.234 |
| HMC |
15 |
2.303 |
0.0416 |
11.079 |
| HMC |
18 |
3.503 |
0.00486 |
12.766 |
| SMC |
5 |
3.284 |
0.00616 |
3.635 |
| SMC |
8 |
4.494 |
0.000843 |
10.379 |
| SMC |
10 |
4.508 |
0.000756 |
7.186 |
| SMC |
12 |
2.620 |
0.0236 |
8.892 |
| SMC |
15 |
3.096 |
0.0101 |
19.432 |
| SMC |
18 |
3.491 |
0.0048 |
7.528 |
| Metro |
5 |
3.566 |
0.00365 |
4.066 |
| Metro |
8 |
5.728 |
4.62e-05 |
4.441 |
| Metro |
10 |
4.230 |
0.00117 |
5.869 |
| Metro |
12 |
2.421 |
0.0291 |
1.862 |
| Metro |
15 |
3.717 |
0.00301 |
5.610 |
| Metro |
18 |
3.631 |
0.00382 |
10.171 |
| DEMetro_Z |
5 |
5.470 |
8.65e-05 |
4.654 |
| DEMetro_Z |
8 |
3.869 |
0.00236 |
6.746 |
| DEMetro_Z |
10 |
2.281 |
0.0432 |
7.980 |
| DEMetro_Z |
12 |
4.614 |
0.000445 |
4.183 |
| DEMetro_Z |
15 |
2.551 |
0.0269 |
27.624 |
| DEMetro_Z |
18 |
3.102 |
0.01 |
23.493 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
1.186
|
0.261
|
0.342
|
| DEMetro_Z_vs_SMC |
1
|
-1.072
|
0.307
|
-0.309
|
| DEMetro_Z_vs_SMC |
2
|
0.287
|
0.78
|
0.083
|
| DEMetro_Z_vs_SMC |
3
|
-1.547
|
0.15
|
-0.447
|
| DEMetro_Z_vs_SMC |
4
|
0.746
|
0.472
|
0.215
|
| DEMetro_Z_vs_SMC |
5
|
2.037
|
0.0665
|
0.588
|
| HMC_vs_Metro |
0
|
-1.794
|
0.1
|
-0.518
|
| HMC_vs_Metro |
1
|
0.785
|
0.449
|
0.227
|
| HMC_vs_Metro |
2
|
1.745
|
0.109
|
0.504
|
| HMC_vs_Metro |
3
|
0.792
|
0.445
|
0.229
|
| HMC_vs_Metro |
4
|
1.067
|
0.309
|
0.308
|
| HMC_vs_Metro |
5
|
0.561
|
0.586
|
0.162
|
| Metro_vs_DEMetro_Z |
0
|
-0.395
|
0.701
|
-0.114
|
| Metro_vs_DEMetro_Z |
1
|
-1.295
|
0.222
|
-0.374
|
| Metro_vs_DEMetro_Z |
2
|
-0.537
|
0.602
|
-0.155
|
| Metro_vs_DEMetro_Z |
3
|
-1.887
|
0.0859
|
-0.545
|
| Metro_vs_DEMetro_Z |
4
|
-2.009
|
0.0697
|
-0.580
|
| Metro_vs_DEMetro_Z |
5
|
-1.638
|
0.13
|
-0.473
|
| HMC_vs_SMC |
0
|
-1.477
|
0.168
|
-0.426
|
| HMC_vs_SMC |
1
|
-1.219
|
0.248
|
-0.352
|
| HMC_vs_SMC |
2
|
1.443
|
0.177
|
0.417
|
| HMC_vs_SMC |
3
|
-1.938
|
0.0787
|
-0.559
|
| HMC_vs_SMC |
4
|
-1.471
|
0.169
|
-0.425
|
| HMC_vs_SMC |
5
|
1.124
|
0.285
|
0.325
|
| Metro_vs_SMC |
0
|
0.243
|
0.812
|
0.070
|
| Metro_vs_SMC |
1
|
-2.135
|
0.0561
|
-0.616
|
| Metro_vs_SMC |
2
|
-0.508
|
0.621
|
-0.147
|
| Metro_vs_SMC |
3
|
-1.922
|
0.0809
|
-0.555
|
| Metro_vs_SMC |
4
|
-2.147
|
0.0549
|
-0.620
|
| Metro_vs_SMC |
5
|
0.895
|
0.39
|
0.258
|
| HMC_vs_DEMetro_Z |
0
|
-2.804
|
0.0171
|
-0.810
|
| HMC_vs_DEMetro_Z |
1
|
-0.233
|
0.82
|
-0.067
|
| HMC_vs_DEMetro_Z |
2
|
0.627
|
0.543
|
0.181
|
| HMC_vs_DEMetro_Z |
3
|
-0.564
|
0.584
|
-0.163
|
| HMC_vs_DEMetro_Z |
4
|
-1.249
|
0.238
|
-0.361
|
| HMC_vs_DEMetro_Z |
5
|
-1.162
|
0.27
|
-0.335
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
0.020 |
0.012 |
0.005 |
1.608 |
| HMC |
8 |
0.033 |
0.010 |
0.004 |
6.220 |
| HMC |
10 |
0.056 |
0.011 |
0.004 |
10.434 |
| HMC |
12 |
0.048 |
0.015 |
0.010 |
3.234 |
| HMC |
15 |
0.057 |
0.010 |
0.004 |
11.079 |
| HMC |
18 |
0.088 |
0.013 |
0.006 |
12.766 |
| SMC |
5 |
0.031 |
0.012 |
0.005 |
3.635 |
| SMC |
8 |
0.048 |
0.010 |
0.004 |
10.379 |
| SMC |
10 |
0.042 |
0.011 |
0.004 |
7.186 |
| SMC |
12 |
0.104 |
0.015 |
0.010 |
8.892 |
| SMC |
15 |
0.092 |
0.010 |
0.004 |
19.432 |
| SMC |
18 |
0.057 |
0.013 |
0.006 |
7.528 |
| Metro |
5 |
0.033 |
0.012 |
0.005 |
4.066 |
| Metro |
8 |
0.027 |
0.010 |
0.004 |
4.441 |
| Metro |
10 |
0.036 |
0.011 |
0.004 |
5.869 |
| Metro |
12 |
0.034 |
0.015 |
0.010 |
1.862 |
| Metro |
15 |
0.034 |
0.010 |
0.004 |
5.610 |
| Metro |
18 |
0.073 |
0.013 |
0.006 |
10.171 |
| DEMetro_Z |
5 |
0.036 |
0.012 |
0.005 |
4.654 |
| DEMetro_Z |
8 |
0.035 |
0.010 |
0.004 |
6.746 |
| DEMetro_Z |
10 |
0.045 |
0.011 |
0.004 |
7.980 |
| DEMetro_Z |
12 |
0.057 |
0.015 |
0.010 |
4.183 |
| DEMetro_Z |
15 |
0.126 |
0.010 |
0.004 |
27.624 |
| DEMetro_Z |
18 |
0.151 |
0.013 |
0.006 |
23.493 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
Mode Transitions
Mode Transitions (scatter)
KDE + Init Plots
Forest & Ridge Plots
Pooled
Chain
Pairwise Scatter Plots
Pooled
Chain
Varying_Tails_with_high_Dimension
(MvStudentT,
nu,
12 runs)
Pooled Chains results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
1.596 |
0.137 |
2.606 |
| HMC |
3.0 |
1.163 |
0.269 |
8.747 |
| HMC |
4.0 |
-3.657 |
0.00157 |
-1.808 |
| HMC |
10.0 |
-2.044 |
0.0536 |
-0.768 |
| HMC |
50.0 |
-3.053 |
0.00584 |
-1.276 |
| SMC |
2.1 |
12.489 |
2.47e-11 |
4.760 |
| SMC |
3.0 |
24.103 |
1.96e-11 |
36.096 |
| SMC |
4.0 |
21.266 |
2.24e-10 |
75.162 |
| SMC |
10.0 |
16.618 |
1.57e-09 |
26.142 |
| SMC |
50.0 |
6.784 |
2.41e-06 |
3.828 |
| Metro |
2.1 |
2.705 |
0.0203 |
12.410 |
| Metro |
3.0 |
6.069 |
6.64e-05 |
11.462 |
| Metro |
4.0 |
8.807 |
1.88e-06 |
16.961 |
| Metro |
10.0 |
12.455 |
2.04e-10 |
6.793 |
| Metro |
50.0 |
8.122 |
3.25e-07 |
4.984 |
| DEMetro_Z |
2.1 |
19.696 |
6.22e-10 |
285.641 |
| DEMetro_Z |
3.0 |
16.588 |
3.93e-09 |
554.963 |
| DEMetro_Z |
4.0 |
19.689 |
6.31e-10 |
865.188 |
| DEMetro_Z |
10.0 |
11.223 |
2.3e-07 |
273.849 |
| DEMetro_Z |
50.0 |
11.533 |
1.74e-07 |
215.971 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
-18.882
|
9.9e-10
|
-5.451
|
| HMC_vs_DEMetro_Z |
1
|
-15.928
|
6.05e-09
|
-4.598
|
| HMC_vs_DEMetro_Z |
2
|
-19.801
|
5.95e-10
|
-5.716
|
| HMC_vs_DEMetro_Z |
3
|
-11.288
|
2.18e-07
|
-3.259
|
| HMC_vs_DEMetro_Z |
4
|
-11.618
|
1.62e-07
|
-3.354
|
| Metro_vs_SMC |
0
|
1.642
|
0.129
|
0.474
|
| Metro_vs_SMC |
1
|
-11.956
|
1.21e-07
|
-3.452
|
| Metro_vs_SMC |
2
|
-13.048
|
4.9e-08
|
-3.767
|
| Metro_vs_SMC |
3
|
-14.707
|
1.4e-08
|
-4.246
|
| Metro_vs_SMC |
4
|
1.552
|
0.149
|
0.448
|
| Metro_vs_DEMetro_Z |
0
|
-17.250
|
2.6e-09
|
-4.980
|
| Metro_vs_DEMetro_Z |
1
|
-16.354
|
4.57e-09
|
-4.721
|
| Metro_vs_DEMetro_Z |
2
|
-19.137
|
8.58e-10
|
-5.524
|
| Metro_vs_DEMetro_Z |
3
|
-10.884
|
3.15e-07
|
-3.142
|
| Metro_vs_DEMetro_Z |
4
|
-11.383
|
2e-07
|
-3.286
|
| HMC_vs_Metro |
0
|
-1.928
|
0.08
|
-0.557
|
| HMC_vs_Metro |
1
|
-0.330
|
0.748
|
-0.095
|
| HMC_vs_Metro |
2
|
-10.010
|
7.32e-07
|
-2.890
|
| HMC_vs_Metro |
3
|
-14.919
|
1.21e-08
|
-4.307
|
| HMC_vs_Metro |
4
|
-11.401
|
1.97e-07
|
-3.291
|
| HMC_vs_SMC |
0
|
-1.423
|
0.183
|
-0.411
|
| HMC_vs_SMC |
1
|
-3.525
|
0.00476
|
-1.018
|
| HMC_vs_SMC |
2
|
-21.295
|
2.72e-10
|
-6.147
|
| HMC_vs_SMC |
3
|
-16.703
|
3.66e-09
|
-4.822
|
| HMC_vs_SMC |
4
|
-8.596
|
3.28e-06
|
-2.481
|
| DEMetro_Z_vs_SMC |
0
|
19.344
|
7.64e-10
|
5.584
|
| DEMetro_Z_vs_SMC |
1
|
15.411
|
8.57e-09
|
4.449
|
| DEMetro_Z_vs_SMC |
2
|
17.963
|
1.69e-09
|
5.186
|
| DEMetro_Z_vs_SMC |
3
|
9.903
|
8.15e-07
|
2.859
|
| DEMetro_Z_vs_SMC |
4
|
11.248
|
2.26e-07
|
3.247
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.140 |
0.071 |
0.027 |
2.606 |
| HMC |
3.0 |
0.074 |
0.037 |
0.004 |
8.747 |
| HMC |
4.0 |
0.028 |
0.031 |
0.002 |
-1.808 |
| HMC |
10.0 |
0.023 |
0.025 |
0.003 |
-0.768 |
| HMC |
50.0 |
0.019 |
0.023 |
0.003 |
-1.276 |
| SMC |
2.1 |
0.197 |
0.071 |
0.027 |
4.760 |
| SMC |
3.0 |
0.190 |
0.037 |
0.004 |
36.096 |
| SMC |
4.0 |
0.182 |
0.031 |
0.002 |
75.162 |
| SMC |
10.0 |
0.112 |
0.025 |
0.003 |
26.142 |
| SMC |
50.0 |
0.035 |
0.023 |
0.003 |
3.828 |
| Metro |
2.1 |
0.401 |
0.071 |
0.027 |
12.410 |
| Metro |
3.0 |
0.085 |
0.037 |
0.004 |
11.462 |
| Metro |
4.0 |
0.065 |
0.031 |
0.002 |
16.961 |
| Metro |
10.0 |
0.048 |
0.025 |
0.003 |
6.793 |
| Metro |
50.0 |
0.039 |
0.023 |
0.003 |
4.984 |
| DEMetro_Z |
2.1 |
7.658 |
0.071 |
0.027 |
285.641 |
| DEMetro_Z |
3.0 |
2.389 |
0.037 |
0.004 |
554.963 |
| DEMetro_Z |
4.0 |
1.768 |
0.031 |
0.002 |
865.188 |
| DEMetro_Z |
10.0 |
0.929 |
0.025 |
0.003 |
273.849 |
| DEMetro_Z |
50.0 |
0.733 |
0.023 |
0.003 |
215.971 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
-0.589 |
0.566 |
-0.176 |
| HMC |
3.0 |
1.099 |
0.295 |
34.663 |
| HMC |
4.0 |
4.162 |
0.00134 |
5.973 |
| HMC |
10.0 |
4.735 |
0.000185 |
2.806 |
| HMC |
50.0 |
4.446 |
0.000225 |
1.641 |
| SMC |
2.1 |
12.941 |
3.8e-09 |
3.980 |
| SMC |
3.0 |
37.485 |
5.74e-13 |
457.548 |
| SMC |
4.0 |
52.469 |
1.48e-14 |
2331.730 |
| SMC |
10.0 |
64.829 |
1.46e-15 |
3486.390 |
| SMC |
50.0 |
41.433 |
1.52e-13 |
158.562 |
| Metro |
2.1 |
1.119 |
0.286 |
2.940 |
| Metro |
3.0 |
2.988 |
0.00972 |
2.433 |
| Metro |
4.0 |
3.452 |
0.00507 |
6.602 |
| Metro |
10.0 |
7.368 |
5.31e-06 |
7.250 |
| Metro |
50.0 |
9.811 |
3.04e-08 |
6.272 |
| DEMetro_Z |
2.1 |
10.611 |
3.52e-07 |
33.717 |
| DEMetro_Z |
3.0 |
10.177 |
6.2e-07 |
383.965 |
| DEMetro_Z |
4.0 |
10.034 |
7.15e-07 |
1207.930 |
| DEMetro_Z |
10.0 |
6.239 |
6.36e-05 |
1215.821 |
| DEMetro_Z |
50.0 |
5.736 |
0.000131 |
1190.490 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
-27.841
|
1.5e-11
|
-8.037
|
| HMC_vs_SMC |
1
|
-12.133
|
1.04e-07
|
-3.503
|
| HMC_vs_SMC |
2
|
-51.865
|
1.68e-14
|
-14.972
|
| HMC_vs_SMC |
3
|
-64.675
|
1.5e-15
|
-18.670
|
| HMC_vs_SMC |
4
|
-39.410
|
3.4e-13
|
-11.377
|
| Metro_vs_DEMetro_Z |
0
|
-6.819
|
2.88e-05
|
-1.968
|
| Metro_vs_DEMetro_Z |
1
|
-10.149
|
6.38e-07
|
-2.930
|
| Metro_vs_DEMetro_Z |
2
|
-9.935
|
7.89e-07
|
-2.868
|
| Metro_vs_DEMetro_Z |
3
|
-6.203
|
6.69e-05
|
-1.791
|
| Metro_vs_DEMetro_Z |
4
|
-5.699
|
0.000138
|
-1.645
|
| HMC_vs_Metro |
0
|
-1.187
|
0.26
|
-0.343
|
| HMC_vs_Metro |
1
|
1.020
|
0.33
|
0.294
|
| HMC_vs_Metro |
2
|
-0.223
|
0.827
|
-0.064
|
| HMC_vs_Metro |
3
|
-4.747
|
0.000603
|
-1.370
|
| HMC_vs_Metro |
4
|
-7.156
|
1.86e-05
|
-2.066
|
| HMC_vs_DEMetro_Z |
0
|
-10.752
|
3.56e-07
|
-3.104
|
| HMC_vs_DEMetro_Z |
1
|
-7.577
|
1.09e-05
|
-2.187
|
| HMC_vs_DEMetro_Z |
2
|
-10.006
|
7.35e-07
|
-2.888
|
| HMC_vs_DEMetro_Z |
3
|
-6.231
|
6.43e-05
|
-1.799
|
| HMC_vs_DEMetro_Z |
4
|
-5.728
|
0.000133
|
-1.653
|
| Metro_vs_SMC |
0
|
-0.404
|
0.694
|
-0.117
|
| Metro_vs_SMC |
1
|
-36.713
|
7.38e-13
|
-10.598
|
| Metro_vs_SMC |
2
|
-51.531
|
1.81e-14
|
-14.876
|
| Metro_vs_SMC |
3
|
-63.934
|
1.7e-15
|
-18.456
|
| Metro_vs_SMC |
4
|
-42.086
|
1.66e-13
|
-12.149
|
| DEMetro_Z_vs_SMC |
0
|
9.220
|
1.65e-06
|
2.662
|
| DEMetro_Z_vs_SMC |
1
|
-1.871
|
0.0881
|
-0.540
|
| DEMetro_Z_vs_SMC |
2
|
-7.912
|
7.26e-06
|
-2.284
|
| DEMetro_Z_vs_SMC |
3
|
-10.810
|
3.38e-07
|
-3.121
|
| DEMetro_Z_vs_SMC |
4
|
4.955
|
0.000432
|
1.431
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
5.622 |
9.632 |
22.759 |
-0.176 |
| HMC |
3.0 |
7.576 |
0.506 |
0.204 |
34.663 |
| HMC |
4.0 |
0.350 |
0.142 |
0.035 |
5.973 |
| HMC |
10.0 |
0.072 |
0.046 |
0.009 |
2.806 |
| HMC |
50.0 |
0.045 |
0.037 |
0.005 |
1.641 |
| SMC |
2.1 |
100.204 |
9.632 |
22.759 |
3.980 |
| SMC |
3.0 |
93.825 |
0.506 |
0.204 |
457.548 |
| SMC |
4.0 |
81.195 |
0.142 |
0.035 |
2331.730 |
| SMC |
10.0 |
31.896 |
0.046 |
0.009 |
3486.390 |
| SMC |
50.0 |
0.799 |
0.037 |
0.005 |
158.562 |
| Metro |
2.1 |
76.540 |
9.632 |
22.759 |
2.940 |
| Metro |
3.0 |
1.003 |
0.506 |
0.204 |
2.433 |
| Metro |
4.0 |
0.371 |
0.142 |
0.035 |
6.602 |
| Metro |
10.0 |
0.112 |
0.046 |
0.009 |
7.250 |
| Metro |
50.0 |
0.067 |
0.037 |
0.005 |
6.272 |
| DEMetro_Z |
2.1 |
776.986 |
9.632 |
22.759 |
33.717 |
| DEMetro_Z |
3.0 |
78.818 |
0.506 |
0.204 |
383.965 |
| DEMetro_Z |
4.0 |
42.131 |
0.142 |
0.035 |
1207.930 |
| DEMetro_Z |
10.0 |
11.153 |
0.046 |
0.009 |
1215.821 |
| DEMetro_Z |
50.0 |
5.760 |
0.037 |
0.005 |
1190.490 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
4.641 |
0.000609 |
7.654 |
| HMC |
3.0 |
1.423 |
0.182 |
100.007 |
| HMC |
4.0 |
3.763 |
0.00297 |
8.658 |
| HMC |
10.0 |
2.099 |
0.0541 |
1.685 |
| HMC |
50.0 |
-0.672 |
0.509 |
-0.304 |
| SMC |
2.1 |
72.581 |
2.55e-16 |
225.703 |
| SMC |
3.0 |
60.175 |
3.29e-15 |
1927.101 |
| SMC |
4.0 |
87.397 |
5.47e-17 |
3137.282 |
| SMC |
10.0 |
108.645 |
4.97e-18 |
2506.727 |
| SMC |
50.0 |
43.163 |
8.88e-14 |
144.275 |
| Metro |
2.1 |
2.491 |
0.03 |
54.418 |
| Metro |
3.0 |
4.892 |
0.000472 |
32.666 |
| Metro |
4.0 |
8.499 |
3.24e-06 |
25.871 |
| Metro |
10.0 |
15.488 |
8.91e-10 |
15.285 |
| Metro |
50.0 |
11.131 |
8.12e-09 |
7.604 |
| DEMetro_Z |
2.1 |
23.824 |
8.09e-11 |
664.602 |
| DEMetro_Z |
3.0 |
20.244 |
4.69e-10 |
1689.311 |
| DEMetro_Z |
4.0 |
20.014 |
5.3e-10 |
2049.604 |
| DEMetro_Z |
10.0 |
15.369 |
8.82e-09 |
1182.294 |
| DEMetro_Z |
50.0 |
9.875 |
8.38e-07 |
614.762 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
-15.727
|
6.92e-09
|
-4.540
|
| Metro_vs_DEMetro_Z |
1
|
-20.207
|
4.79e-10
|
-5.833
|
| Metro_vs_DEMetro_Z |
2
|
-19.740
|
6.15e-10
|
-5.699
|
| Metro_vs_DEMetro_Z |
3
|
-15.111
|
1.05e-08
|
-4.362
|
| Metro_vs_DEMetro_Z |
4
|
-9.760
|
9.42e-07
|
-2.818
|
| DEMetro_Z_vs_SMC |
0
|
14.890
|
1.23e-08
|
4.298
|
| DEMetro_Z_vs_SMC |
1
|
-2.663
|
0.0221
|
-0.769
|
| DEMetro_Z_vs_SMC |
2
|
-9.151
|
1.78e-06
|
-2.642
|
| DEMetro_Z_vs_SMC |
3
|
-15.952
|
5.95e-09
|
-4.605
|
| DEMetro_Z_vs_SMC |
4
|
7.494
|
1.21e-05
|
2.163
|
| HMC_vs_DEMetro_Z |
0
|
-23.459
|
9.6e-11
|
-6.772
|
| HMC_vs_DEMetro_Z |
1
|
-14.721
|
1.39e-08
|
-4.250
|
| HMC_vs_DEMetro_Z |
2
|
-20.041
|
5.23e-10
|
-5.785
|
| HMC_vs_DEMetro_Z |
3
|
-15.396
|
8.66e-09
|
-4.444
|
| HMC_vs_DEMetro_Z |
4
|
-9.891
|
8.25e-07
|
-2.855
|
| HMC_vs_Metro |
0
|
-2.084
|
0.0612
|
-0.602
|
| HMC_vs_Metro |
1
|
0.929
|
0.373
|
0.268
|
| HMC_vs_Metro |
2
|
-3.775
|
0.00307
|
-1.090
|
| HMC_vs_Metro |
3
|
-10.809
|
3.38e-07
|
-3.120
|
| HMC_vs_Metro |
4
|
-13.647
|
3.07e-08
|
-3.940
|
| HMC_vs_SMC |
0
|
-64.343
|
1.58e-15
|
-18.574
|
| HMC_vs_SMC |
1
|
-23.727
|
8.48e-11
|
-6.850
|
| HMC_vs_SMC |
2
|
-85.284
|
7.18e-17
|
-24.619
|
| HMC_vs_SMC |
3
|
-108.641
|
5.02e-18
|
-31.362
|
| HMC_vs_SMC |
4
|
-43.798
|
1.07e-13
|
-12.643
|
| Metro_vs_SMC |
0
|
-8.107
|
5.75e-06
|
-2.340
|
| Metro_vs_SMC |
1
|
-58.857
|
4.21e-15
|
-16.990
|
| Metro_vs_SMC |
2
|
-84.395
|
8.06e-17
|
-24.363
|
| Metro_vs_SMC |
3
|
-107.662
|
5.55e-18
|
-31.079
|
| Metro_vs_SMC |
4
|
-40.155
|
2.77e-13
|
-11.592
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.340 |
0.113 |
0.030 |
7.654 |
| HMC |
3.0 |
0.401 |
0.063 |
0.003 |
100.007 |
| HMC |
4.0 |
0.065 |
0.048 |
0.002 |
8.658 |
| HMC |
10.0 |
0.037 |
0.035 |
0.001 |
1.685 |
| HMC |
50.0 |
0.029 |
0.030 |
0.002 |
-0.304 |
| SMC |
2.1 |
6.811 |
0.113 |
0.030 |
225.703 |
| SMC |
3.0 |
6.565 |
0.063 |
0.003 |
1927.101 |
| SMC |
4.0 |
6.120 |
0.048 |
0.002 |
3137.282 |
| SMC |
10.0 |
3.698 |
0.035 |
0.001 |
2506.727 |
| SMC |
50.0 |
0.275 |
0.030 |
0.002 |
144.275 |
| Metro |
2.1 |
1.728 |
0.113 |
0.030 |
54.418 |
| Metro |
3.0 |
0.173 |
0.063 |
0.003 |
32.666 |
| Metro |
4.0 |
0.098 |
0.048 |
0.002 |
25.871 |
| Metro |
10.0 |
0.057 |
0.035 |
0.001 |
15.285 |
| Metro |
50.0 |
0.043 |
0.030 |
0.002 |
7.604 |
| DEMetro_Z |
2.1 |
19.835 |
0.113 |
0.030 |
664.602 |
| DEMetro_Z |
3.0 |
5.763 |
0.063 |
0.003 |
1689.311 |
| DEMetro_Z |
4.0 |
4.015 |
0.048 |
0.002 |
2049.604 |
| DEMetro_Z |
10.0 |
1.762 |
0.035 |
0.001 |
1182.294 |
| DEMetro_Z |
50.0 |
1.075 |
0.030 |
0.002 |
614.762 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
3.983 |
0.00215 |
70.392 |
| HMC |
3.0 |
2.461 |
0.0316 |
31.981 |
| HMC |
4.0 |
3.252 |
0.00724 |
5.841 |
| HMC |
10.0 |
1.240 |
0.233 |
0.845 |
| HMC |
50.0 |
-1.265 |
0.219 |
-0.517 |
| SMC |
2.1 |
131.350 |
3.01e-19 |
375.972 |
| SMC |
3.0 |
70.579 |
4.28e-16 |
285.193 |
| SMC |
4.0 |
129.077 |
4.25e-19 |
414.167 |
| SMC |
10.0 |
77.545 |
1.46e-16 |
298.316 |
| SMC |
50.0 |
42.827 |
2.1e-14 |
62.321 |
| Metro |
2.1 |
7.324 |
1.49e-05 |
169.487 |
| Metro |
3.0 |
5.270 |
0.000259 |
28.240 |
| Metro |
4.0 |
9.447 |
1.07e-06 |
23.957 |
| Metro |
10.0 |
14.379 |
4.01e-10 |
10.599 |
| Metro |
50.0 |
10.349 |
7e-09 |
6.019 |
| DEMetro_Z |
2.1 |
55.783 |
7.12e-15 |
462.986 |
| DEMetro_Z |
3.0 |
65.115 |
1.16e-15 |
329.625 |
| DEMetro_Z |
4.0 |
51.789 |
1.63e-14 |
479.572 |
| DEMetro_Z |
10.0 |
35.821 |
9.21e-13 |
310.084 |
| DEMetro_Z |
50.0 |
18.029 |
1.6e-09 |
214.204 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
9.696
|
1.01e-06
|
2.799
|
| DEMetro_Z_vs_SMC |
1
|
6.990
|
2.3e-05
|
2.018
|
| DEMetro_Z_vs_SMC |
2
|
6.388
|
5.16e-05
|
1.844
|
| DEMetro_Z_vs_SMC |
3
|
1.283
|
0.226
|
0.371
|
| DEMetro_Z_vs_SMC |
4
|
12.391
|
8.36e-08
|
3.577
|
| HMC_vs_Metro |
0
|
-3.349
|
0.00649
|
-0.967
|
| HMC_vs_Metro |
1
|
0.244
|
0.811
|
0.071
|
| HMC_vs_Metro |
2
|
-5.243
|
0.000276
|
-1.513
|
| HMC_vs_Metro |
3
|
-10.140
|
6.43e-07
|
-2.927
|
| HMC_vs_Metro |
4
|
-11.957
|
1.21e-07
|
-3.452
|
| Metro_vs_DEMetro_Z |
0
|
-11.886
|
1.28e-07
|
-3.431
|
| Metro_vs_DEMetro_Z |
1
|
-58.457
|
4.54e-15
|
-16.875
|
| Metro_vs_DEMetro_Z |
2
|
-50.273
|
2.37e-14
|
-14.513
|
| Metro_vs_DEMetro_Z |
3
|
-35.076
|
1.21e-12
|
-10.126
|
| Metro_vs_DEMetro_Z |
4
|
-17.648
|
2.04e-09
|
-5.095
|
| HMC_vs_SMC |
0
|
-15.694
|
7.07e-09
|
-4.531
|
| HMC_vs_SMC |
1
|
-23.151
|
1.11e-10
|
-6.683
|
| HMC_vs_SMC |
2
|
-105.119
|
7.22e-18
|
-30.345
|
| HMC_vs_SMC |
3
|
-75.862
|
2.6e-16
|
-21.899
|
| HMC_vs_SMC |
4
|
-44.714
|
8.55e-14
|
-12.908
|
| Metro_vs_SMC |
0
|
-8.609
|
3.23e-06
|
-2.485
|
| Metro_vs_SMC |
1
|
-39.162
|
3.65e-13
|
-11.305
|
| Metro_vs_SMC |
2
|
-96.209
|
1.91e-17
|
-27.773
|
| Metro_vs_SMC |
3
|
-77.592
|
2.03e-16
|
-22.399
|
| Metro_vs_SMC |
4
|
-37.335
|
6.14e-13
|
-10.778
|
| HMC_vs_DEMetro_Z |
0
|
-20.535
|
4.03e-10
|
-5.928
|
| HMC_vs_DEMetro_Z |
1
|
-19.718
|
6.22e-10
|
-5.692
|
| HMC_vs_DEMetro_Z |
2
|
-49.684
|
2.7e-14
|
-14.343
|
| HMC_vs_DEMetro_Z |
3
|
-35.790
|
9.74e-13
|
-10.332
|
| HMC_vs_DEMetro_Z |
4
|
-18.126
|
1.53e-09
|
-5.232
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.085 |
0.015 |
0.001 |
70.392 |
| HMC |
3.0 |
0.059 |
0.015 |
0.001 |
31.981 |
| HMC |
4.0 |
0.020 |
0.014 |
0.001 |
5.841 |
| HMC |
10.0 |
0.016 |
0.015 |
0.001 |
0.845 |
| HMC |
50.0 |
0.013 |
0.014 |
0.002 |
-0.517 |
| SMC |
2.1 |
0.390 |
0.015 |
0.001 |
375.972 |
| SMC |
3.0 |
0.402 |
0.015 |
0.001 |
285.193 |
| SMC |
4.0 |
0.401 |
0.014 |
0.001 |
414.167 |
| SMC |
10.0 |
0.382 |
0.015 |
0.001 |
298.316 |
| SMC |
50.0 |
0.114 |
0.014 |
0.002 |
62.321 |
| Metro |
2.1 |
0.184 |
0.015 |
0.001 |
169.487 |
| Metro |
3.0 |
0.054 |
0.015 |
0.001 |
28.240 |
| Metro |
4.0 |
0.037 |
0.014 |
0.001 |
23.957 |
| Metro |
10.0 |
0.028 |
0.015 |
0.001 |
10.599 |
| Metro |
50.0 |
0.024 |
0.014 |
0.002 |
6.019 |
| DEMetro_Z |
2.1 |
0.476 |
0.015 |
0.001 |
462.986 |
| DEMetro_Z |
3.0 |
0.463 |
0.015 |
0.001 |
329.625 |
| DEMetro_Z |
4.0 |
0.463 |
0.014 |
0.001 |
479.572 |
| DEMetro_Z |
10.0 |
0.396 |
0.015 |
0.001 |
310.084 |
| DEMetro_Z |
50.0 |
0.356 |
0.014 |
0.002 |
214.204 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
R Hat (scatter)
Mode Transitions
One Chain results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
1.208 |
0.252 |
22.271 |
| HMC |
3.0 |
0.131 |
0.897 |
0.075 |
| HMC |
4.0 |
-2.697 |
0.0138 |
-1.320 |
| HMC |
10.0 |
-2.420 |
0.0242 |
-0.987 |
| HMC |
50.0 |
-3.461 |
0.00296 |
-1.140 |
| SMC |
2.1 |
15.137 |
9.92e-13 |
7.048 |
| SMC |
3.0 |
16.690 |
2.11e-09 |
33.317 |
| SMC |
4.0 |
25.255 |
3.17e-11 |
77.619 |
| SMC |
10.0 |
25.943 |
1.36e-12 |
25.754 |
| SMC |
50.0 |
5.539 |
2.93e-05 |
3.108 |
| Metro |
2.1 |
4.219 |
0.00114 |
5.262 |
| Metro |
3.0 |
5.148 |
0.000289 |
11.958 |
| Metro |
4.0 |
10.266 |
3.24e-07 |
16.322 |
| Metro |
10.0 |
10.252 |
6.16e-08 |
8.272 |
| Metro |
50.0 |
12.836 |
1.74e-11 |
5.806 |
| DEMetro_Z |
2.1 |
11.427 |
1.91e-07 |
276.091 |
| DEMetro_Z |
3.0 |
10.803 |
3.4e-07 |
482.510 |
| DEMetro_Z |
4.0 |
18.831 |
1.02e-09 |
839.502 |
| DEMetro_Z |
10.0 |
10.606 |
4.09e-07 |
273.330 |
| DEMetro_Z |
50.0 |
12.285 |
9.07e-08 |
186.415 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
-7.651
|
9.96e-06
|
-2.209
|
| HMC_vs_DEMetro_Z |
1
|
-10.840
|
3.28e-07
|
-3.129
|
| HMC_vs_DEMetro_Z |
2
|
-18.896
|
9.82e-10
|
-5.455
|
| HMC_vs_DEMetro_Z |
3
|
-10.649
|
3.93e-07
|
-3.074
|
| HMC_vs_DEMetro_Z |
4
|
-12.428
|
8.11e-08
|
-3.588
|
| Metro_vs_SMC |
0
|
-1.328
|
0.211
|
-0.383
|
| Metro_vs_SMC |
1
|
-8.608
|
3.24e-06
|
-2.485
|
| Metro_vs_SMC |
2
|
-21.599
|
2.34e-10
|
-6.235
|
| Metro_vs_SMC |
3
|
-13.124
|
4.61e-08
|
-3.788
|
| Metro_vs_SMC |
4
|
4.648
|
0.000707
|
1.342
|
| Metro_vs_DEMetro_Z |
0
|
-11.082
|
2.63e-07
|
-3.199
|
| Metro_vs_DEMetro_Z |
1
|
-10.542
|
4.35e-07
|
-3.043
|
| Metro_vs_DEMetro_Z |
2
|
-18.276
|
1.4e-09
|
-5.276
|
| Metro_vs_DEMetro_Z |
3
|
-10.323
|
5.38e-07
|
-2.980
|
| Metro_vs_DEMetro_Z |
4
|
-11.984
|
1.18e-07
|
-3.460
|
| HMC_vs_Metro |
0
|
0.931
|
0.372
|
0.269
|
| HMC_vs_Metro |
1
|
-5.082
|
0.000354
|
-1.467
|
| HMC_vs_Metro |
2
|
-11.026
|
2.76e-07
|
-3.183
|
| HMC_vs_Metro |
3
|
-10.655
|
3.91e-07
|
-3.076
|
| HMC_vs_Metro |
4
|
-18.911
|
9.74e-10
|
-5.459
|
| HMC_vs_SMC |
0
|
0.828
|
0.425
|
0.239
|
| HMC_vs_SMC |
1
|
-15.562
|
7.73e-09
|
-4.492
|
| HMC_vs_SMC |
2
|
-24.974
|
4.88e-11
|
-7.209
|
| HMC_vs_SMC |
3
|
-31.715
|
3.64e-12
|
-9.155
|
| HMC_vs_SMC |
4
|
-10.293
|
5.54e-07
|
-2.971
|
| DEMetro_Z_vs_SMC |
0
|
11.165
|
2.43e-07
|
3.223
|
| DEMetro_Z_vs_SMC |
1
|
10.230
|
5.88e-07
|
2.953
|
| DEMetro_Z_vs_SMC |
2
|
17.138
|
2.78e-09
|
4.947
|
| DEMetro_Z_vs_SMC |
3
|
9.782
|
9.21e-07
|
2.824
|
| DEMetro_Z_vs_SMC |
4
|
12.149
|
1.02e-07
|
3.507
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.663 |
0.071 |
0.027 |
22.271 |
| HMC |
3.0 |
0.037 |
0.037 |
0.004 |
0.075 |
| HMC |
4.0 |
0.029 |
0.031 |
0.002 |
-1.320 |
| HMC |
10.0 |
0.022 |
0.025 |
0.003 |
-0.987 |
| HMC |
50.0 |
0.019 |
0.023 |
0.003 |
-1.140 |
| SMC |
2.1 |
0.258 |
0.071 |
0.027 |
7.048 |
| SMC |
3.0 |
0.178 |
0.037 |
0.004 |
33.317 |
| SMC |
4.0 |
0.187 |
0.031 |
0.002 |
77.619 |
| SMC |
10.0 |
0.110 |
0.025 |
0.003 |
25.754 |
| SMC |
50.0 |
0.033 |
0.023 |
0.003 |
3.108 |
| Metro |
2.1 |
0.211 |
0.071 |
0.027 |
5.262 |
| Metro |
3.0 |
0.087 |
0.037 |
0.004 |
11.958 |
| Metro |
4.0 |
0.064 |
0.031 |
0.002 |
16.322 |
| Metro |
10.0 |
0.053 |
0.025 |
0.003 |
8.272 |
| Metro |
50.0 |
0.042 |
0.023 |
0.003 |
5.806 |
| DEMetro_Z |
2.1 |
7.404 |
0.071 |
0.027 |
276.091 |
| DEMetro_Z |
3.0 |
2.082 |
0.037 |
0.004 |
482.510 |
| DEMetro_Z |
4.0 |
1.717 |
0.031 |
0.002 |
839.502 |
| DEMetro_Z |
10.0 |
0.928 |
0.025 |
0.003 |
273.330 |
| DEMetro_Z |
50.0 |
0.635 |
0.023 |
0.003 |
186.415 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
1.086 |
0.293 |
0.704 |
| HMC |
3.0 |
1.825 |
0.0842 |
0.992 |
| HMC |
4.0 |
3.098 |
0.00811 |
2.749 |
| HMC |
10.0 |
3.810 |
0.00137 |
2.261 |
| HMC |
50.0 |
4.175 |
0.000418 |
1.889 |
| SMC |
2.1 |
14.493 |
1.93e-09 |
4.380 |
| SMC |
3.0 |
28.146 |
1.32e-11 |
421.706 |
| SMC |
4.0 |
34.168 |
1.62e-12 |
2268.486 |
| SMC |
10.0 |
33.488 |
2.01e-12 |
3164.149 |
| SMC |
50.0 |
14.982 |
1.12e-08 |
115.994 |
| Metro |
2.1 |
0.081 |
0.936 |
0.025 |
| Metro |
3.0 |
1.809 |
0.0962 |
2.982 |
| Metro |
4.0 |
7.255 |
1.21e-05 |
12.711 |
| Metro |
10.0 |
9.537 |
1.11e-07 |
7.171 |
| Metro |
50.0 |
14.230 |
4.42e-12 |
6.816 |
| DEMetro_Z |
2.1 |
6.746 |
2.8e-05 |
17.221 |
| DEMetro_Z |
3.0 |
5.812 |
0.000117 |
152.676 |
| DEMetro_Z |
4.0 |
9.772 |
9.3e-07 |
572.254 |
| DEMetro_Z |
10.0 |
4.697 |
0.000654 |
399.180 |
| DEMetro_Z |
50.0 |
4.179 |
0.00154 |
421.943 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
-5.761
|
0.000126
|
-1.663
|
| HMC_vs_SMC |
1
|
-28.049
|
1.38e-11
|
-8.097
|
| HMC_vs_SMC |
2
|
-34.301
|
1.55e-12
|
-9.902
|
| HMC_vs_SMC |
3
|
-33.476
|
2.02e-12
|
-9.664
|
| HMC_vs_SMC |
4
|
-14.716
|
1.39e-08
|
-4.248
|
| Metro_vs_DEMetro_Z |
0
|
-6.692
|
3.41e-05
|
-1.932
|
| Metro_vs_DEMetro_Z |
1
|
-5.751
|
0.000128
|
-1.660
|
| Metro_vs_DEMetro_Z |
2
|
-9.476
|
1.26e-06
|
-2.735
|
| Metro_vs_DEMetro_Z |
3
|
-4.626
|
0.000733
|
-1.335
|
| Metro_vs_DEMetro_Z |
4
|
-4.111
|
0.00173
|
-1.187
|
| HMC_vs_Metro |
0
|
1.179
|
0.263
|
0.340
|
| HMC_vs_Metro |
1
|
-1.326
|
0.212
|
-0.383
|
| HMC_vs_Metro |
2
|
-4.852
|
0.000509
|
-1.401
|
| HMC_vs_Metro |
3
|
-6.592
|
3.91e-05
|
-1.903
|
| HMC_vs_Metro |
4
|
-9.611
|
1.1e-06
|
-2.774
|
| HMC_vs_DEMetro_Z |
0
|
-6.016
|
8.73e-05
|
-1.737
|
| HMC_vs_DEMetro_Z |
1
|
-5.780
|
0.000123
|
-1.668
|
| HMC_vs_DEMetro_Z |
2
|
-9.775
|
9.27e-07
|
-2.822
|
| HMC_vs_DEMetro_Z |
3
|
-4.671
|
0.000681
|
-1.348
|
| HMC_vs_DEMetro_Z |
4
|
-4.163
|
0.00158
|
-1.202
|
| Metro_vs_SMC |
0
|
-26.425
|
2.65e-11
|
-7.628
|
| Metro_vs_SMC |
1
|
-26.598
|
2.46e-11
|
-7.678
|
| Metro_vs_SMC |
2
|
-33.555
|
1.97e-12
|
-9.687
|
| Metro_vs_SMC |
3
|
-33.385
|
2.08e-12
|
-9.638
|
| Metro_vs_SMC |
4
|
-14.072
|
2.23e-08
|
-4.062
|
| DEMetro_Z_vs_SMC |
0
|
5.112
|
0.000338
|
1.476
|
| DEMetro_Z_vs_SMC |
1
|
-8.040
|
6.23e-06
|
-2.321
|
| DEMetro_Z_vs_SMC |
2
|
-22.709
|
1.36e-10
|
-6.555
|
| DEMetro_Z_vs_SMC |
3
|
-26.997
|
2.1e-11
|
-7.793
|
| DEMetro_Z_vs_SMC |
4
|
3.076
|
0.0105
|
0.888
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
25.661 |
9.632 |
22.759 |
0.704 |
| HMC |
3.0 |
0.709 |
0.506 |
0.204 |
0.992 |
| HMC |
4.0 |
0.238 |
0.142 |
0.035 |
2.749 |
| HMC |
10.0 |
0.067 |
0.046 |
0.009 |
2.261 |
| HMC |
50.0 |
0.046 |
0.037 |
0.005 |
1.889 |
| SMC |
2.1 |
109.311 |
9.632 |
22.759 |
4.380 |
| SMC |
3.0 |
86.515 |
0.506 |
0.204 |
421.706 |
| SMC |
4.0 |
78.996 |
0.142 |
0.035 |
2268.486 |
| SMC |
10.0 |
28.952 |
0.046 |
0.009 |
3164.149 |
| SMC |
50.0 |
0.594 |
0.037 |
0.005 |
115.994 |
| Metro |
2.1 |
10.198 |
9.632 |
22.759 |
0.025 |
| Metro |
3.0 |
1.114 |
0.506 |
0.204 |
2.982 |
| Metro |
4.0 |
0.584 |
0.142 |
0.035 |
12.711 |
| Metro |
10.0 |
0.112 |
0.046 |
0.009 |
7.171 |
| Metro |
50.0 |
0.069 |
0.037 |
0.005 |
6.816 |
| DEMetro_Z |
2.1 |
401.563 |
9.632 |
22.759 |
17.221 |
| DEMetro_Z |
3.0 |
31.645 |
0.506 |
0.204 |
152.676 |
| DEMetro_Z |
4.0 |
20.034 |
0.142 |
0.035 |
572.254 |
| DEMetro_Z |
10.0 |
3.693 |
0.046 |
0.009 |
399.180 |
| DEMetro_Z |
50.0 |
2.065 |
0.037 |
0.005 |
421.943 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
2.006 |
0.07 |
51.682 |
| HMC |
3.0 |
3.487 |
0.00475 |
6.609 |
| HMC |
4.0 |
2.958 |
0.0127 |
7.318 |
| HMC |
10.0 |
1.304 |
0.211 |
0.847 |
| HMC |
50.0 |
0.076 |
0.94 |
0.026 |
| SMC |
2.1 |
107.341 |
1.76e-18 |
233.885 |
| SMC |
3.0 |
46.063 |
6.16e-14 |
1810.192 |
| SMC |
4.0 |
57.894 |
5.04e-15 |
3054.026 |
| SMC |
10.0 |
53.263 |
1.26e-14 |
2366.197 |
| SMC |
50.0 |
15.484 |
7.81e-09 |
108.270 |
| Metro |
2.1 |
3.722 |
0.00332 |
17.083 |
| Metro |
3.0 |
2.523 |
0.0283 |
38.224 |
| Metro |
4.0 |
10.613 |
3.65e-07 |
38.890 |
| Metro |
10.0 |
11.407 |
1.01e-07 |
17.693 |
| Metro |
50.0 |
13.536 |
2.88e-10 |
8.685 |
| DEMetro_Z |
2.1 |
14.001 |
2.35e-08 |
487.328 |
| DEMetro_Z |
3.0 |
9.161 |
1.76e-06 |
988.796 |
| DEMetro_Z |
4.0 |
16.760 |
3.53e-09 |
1377.139 |
| DEMetro_Z |
10.0 |
10.034 |
7.15e-07 |
699.782 |
| DEMetro_Z |
50.0 |
11.030 |
2.75e-07 |
363.622 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
-13.077
|
4.79e-08
|
-3.775
|
| Metro_vs_DEMetro_Z |
1
|
-8.756
|
2.74e-06
|
-2.528
|
| Metro_vs_DEMetro_Z |
2
|
-16.187
|
5.1e-09
|
-4.673
|
| Metro_vs_DEMetro_Z |
3
|
-9.860
|
8.51e-07
|
-2.846
|
| Metro_vs_DEMetro_Z |
4
|
-10.811
|
3.37e-07
|
-3.121
|
| DEMetro_Z_vs_SMC |
0
|
7.302
|
1.54e-05
|
2.108
|
| DEMetro_Z_vs_SMC |
1
|
-6.646
|
3.63e-05
|
-1.919
|
| DEMetro_Z_vs_SMC |
2
|
-21.212
|
2.84e-10
|
-6.123
|
| DEMetro_Z_vs_SMC |
3
|
-22.180
|
1.76e-10
|
-6.403
|
| DEMetro_Z_vs_SMC |
4
|
8.180
|
5.28e-06
|
2.361
|
| HMC_vs_DEMetro_Z |
0
|
-8.803
|
2.6e-06
|
-2.541
|
| HMC_vs_DEMetro_Z |
1
|
-9.153
|
1.78e-06
|
-2.642
|
| HMC_vs_DEMetro_Z |
2
|
-16.771
|
3.5e-09
|
-4.841
|
| HMC_vs_DEMetro_Z |
3
|
-10.020
|
7.25e-07
|
-2.892
|
| HMC_vs_DEMetro_Z |
4
|
-11.060
|
2.68e-07
|
-3.193
|
| HMC_vs_Metro |
0
|
1.340
|
0.207
|
0.387
|
| HMC_vs_Metro |
1
|
-2.054
|
0.0645
|
-0.593
|
| HMC_vs_Metro |
2
|
-6.483
|
4.53e-05
|
-1.871
|
| HMC_vs_Metro |
3
|
-9.872
|
8.4e-07
|
-2.850
|
| HMC_vs_Metro |
4
|
-16.207
|
5.03e-09
|
-4.679
|
| HMC_vs_SMC |
0
|
-6.786
|
3.01e-05
|
-1.959
|
| HMC_vs_SMC |
1
|
-46.428
|
5.67e-14
|
-13.403
|
| HMC_vs_SMC |
2
|
-59.329
|
3.86e-15
|
-17.127
|
| HMC_vs_SMC |
3
|
-53.452
|
1.21e-14
|
-15.430
|
| HMC_vs_SMC |
4
|
-15.571
|
7.68e-09
|
-4.495
|
| Metro_vs_SMC |
0
|
-42.411
|
1.53e-13
|
-12.243
|
| Metro_vs_SMC |
1
|
-36.795
|
7.2e-13
|
-10.622
|
| Metro_vs_SMC |
2
|
-55.708
|
7.69e-15
|
-16.082
|
| Metro_vs_SMC |
3
|
-52.752
|
1.4e-14
|
-15.228
|
| Metro_vs_SMC |
4
|
-14.214
|
2.01e-08
|
-4.103
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
1.647 |
0.113 |
0.030 |
51.682 |
| HMC |
3.0 |
0.085 |
0.063 |
0.003 |
6.609 |
| HMC |
4.0 |
0.062 |
0.048 |
0.002 |
7.318 |
| HMC |
10.0 |
0.036 |
0.035 |
0.001 |
0.847 |
| HMC |
50.0 |
0.030 |
0.030 |
0.002 |
0.026 |
| SMC |
2.1 |
7.054 |
0.113 |
0.030 |
233.885 |
| SMC |
3.0 |
6.171 |
0.063 |
0.003 |
1810.192 |
| SMC |
4.0 |
5.959 |
0.048 |
0.002 |
3054.026 |
| SMC |
10.0 |
3.492 |
0.035 |
0.001 |
2366.197 |
| SMC |
50.0 |
0.214 |
0.030 |
0.002 |
108.270 |
| Metro |
2.1 |
0.620 |
0.113 |
0.030 |
17.083 |
| Metro |
3.0 |
0.192 |
0.063 |
0.003 |
38.224 |
| Metro |
4.0 |
0.123 |
0.048 |
0.002 |
38.890 |
| Metro |
10.0 |
0.060 |
0.035 |
0.001 |
17.693 |
| Metro |
50.0 |
0.045 |
0.030 |
0.002 |
8.685 |
| DEMetro_Z |
2.1 |
14.575 |
0.113 |
0.030 |
487.328 |
| DEMetro_Z |
3.0 |
3.399 |
0.063 |
0.003 |
988.796 |
| DEMetro_Z |
4.0 |
2.713 |
0.048 |
0.002 |
1377.139 |
| DEMetro_Z |
10.0 |
1.057 |
0.035 |
0.001 |
699.782 |
| DEMetro_Z |
50.0 |
0.648 |
0.030 |
0.002 |
363.622 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
1.999 |
0.0709 |
158.396 |
| HMC |
3.0 |
2.093 |
0.0591 |
3.693 |
| HMC |
4.0 |
2.605 |
0.0238 |
5.598 |
| HMC |
10.0 |
0.470 |
0.644 |
0.278 |
| HMC |
50.0 |
-1.058 |
0.305 |
-0.345 |
| SMC |
2.1 |
68.670 |
6.7e-16 |
390.953 |
| SMC |
3.0 |
107.307 |
2.76e-18 |
295.980 |
| SMC |
4.0 |
80.205 |
1.19e-16 |
435.426 |
| SMC |
10.0 |
140.891 |
7.39e-20 |
298.961 |
| SMC |
50.0 |
17.790 |
1.36e-09 |
47.903 |
| Metro |
2.1 |
5.030 |
0.000384 |
82.876 |
| Metro |
3.0 |
3.353 |
0.00643 |
30.151 |
| Metro |
4.0 |
9.890 |
7.33e-07 |
33.265 |
| Metro |
10.0 |
13.640 |
2.86e-09 |
12.314 |
| Metro |
50.0 |
15.170 |
4.48e-13 |
6.486 |
| DEMetro_Z |
2.1 |
27.731 |
1.55e-11 |
512.316 |
| DEMetro_Z |
3.0 |
25.640 |
3.6e-11 |
331.008 |
| DEMetro_Z |
4.0 |
46.360 |
5.55e-14 |
479.131 |
| DEMetro_Z |
10.0 |
16.548 |
4.01e-09 |
297.622 |
| DEMetro_Z |
50.0 |
25.866 |
3.12e-11 |
170.418 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
6.042
|
8.4e-05
|
1.744
|
| DEMetro_Z_vs_SMC |
1
|
2.532
|
0.0279
|
0.731
|
| DEMetro_Z_vs_SMC |
2
|
3.138
|
0.00945
|
0.906
|
| DEMetro_Z_vs_SMC |
3
|
-0.075
|
0.941
|
-0.022
|
| DEMetro_Z_vs_SMC |
4
|
20.347
|
4.44e-10
|
5.874
|
| HMC_vs_Metro |
0
|
1.026
|
0.327
|
0.296
|
| HMC_vs_Metro |
1
|
-2.742
|
0.0192
|
-0.792
|
| HMC_vs_Metro |
2
|
-7.082
|
2.04e-05
|
-2.045
|
| HMC_vs_Metro |
3
|
-11.791
|
1.39e-07
|
-3.404
|
| HMC_vs_Metro |
4
|
-21.887
|
2.03e-10
|
-6.318
|
| Metro_vs_DEMetro_Z |
0
|
-20.439
|
4.23e-10
|
-5.900
|
| Metro_vs_DEMetro_Z |
1
|
-27.606
|
1.65e-11
|
-7.969
|
| Metro_vs_DEMetro_Z |
2
|
-38.174
|
4.82e-13
|
-11.020
|
| Metro_vs_DEMetro_Z |
3
|
-16.147
|
5.24e-09
|
-4.661
|
| Metro_vs_DEMetro_Z |
4
|
-25.561
|
3.79e-11
|
-7.379
|
| HMC_vs_SMC |
0
|
-2.939
|
0.0135
|
-0.849
|
| HMC_vs_SMC |
1
|
-97.171
|
1.71e-17
|
-28.051
|
| HMC_vs_SMC |
2
|
-78.286
|
1.84e-16
|
-22.599
|
| HMC_vs_SMC |
3
|
-133.505
|
5.21e-19
|
-38.539
|
| HMC_vs_SMC |
4
|
-18.248
|
1.43e-09
|
-5.268
|
| Metro_vs_SMC |
0
|
-15.954
|
5.95e-09
|
-4.605
|
| Metro_vs_SMC |
1
|
-28.184
|
1.31e-11
|
-8.136
|
| Metro_vs_SMC |
2
|
-67.339
|
9.61e-16
|
-19.439
|
| Metro_vs_SMC |
3
|
-127.001
|
9.03e-19
|
-36.662
|
| Metro_vs_SMC |
4
|
-15.103
|
1.06e-08
|
-4.360
|
| HMC_vs_DEMetro_Z |
0
|
-4.040
|
0.00195
|
-1.166
|
| HMC_vs_DEMetro_Z |
1
|
-25.610
|
3.71e-11
|
-7.393
|
| HMC_vs_DEMetro_Z |
2
|
-48.257
|
3.71e-14
|
-13.931
|
| HMC_vs_DEMetro_Z |
3
|
-16.586
|
3.94e-09
|
-4.788
|
| HMC_vs_DEMetro_Z |
4
|
-26.249
|
2.84e-11
|
-7.577
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.173 |
0.015 |
0.001 |
158.396 |
| HMC |
3.0 |
0.020 |
0.015 |
0.001 |
3.693 |
| HMC |
4.0 |
0.019 |
0.014 |
0.001 |
5.598 |
| HMC |
10.0 |
0.015 |
0.015 |
0.001 |
0.278 |
| HMC |
50.0 |
0.014 |
0.014 |
0.002 |
-0.345 |
| SMC |
2.1 |
0.405 |
0.015 |
0.001 |
390.953 |
| SMC |
3.0 |
0.417 |
0.015 |
0.001 |
295.980 |
| SMC |
4.0 |
0.421 |
0.014 |
0.001 |
435.426 |
| SMC |
10.0 |
0.383 |
0.015 |
0.001 |
298.961 |
| SMC |
50.0 |
0.091 |
0.014 |
0.002 |
47.903 |
| Metro |
2.1 |
0.097 |
0.015 |
0.001 |
82.876 |
| Metro |
3.0 |
0.056 |
0.015 |
0.001 |
30.151 |
| Metro |
4.0 |
0.045 |
0.014 |
0.001 |
33.265 |
| Metro |
10.0 |
0.030 |
0.015 |
0.001 |
12.314 |
| Metro |
50.0 |
0.025 |
0.014 |
0.002 |
6.486 |
| DEMetro_Z |
2.1 |
0.526 |
0.015 |
0.001 |
512.316 |
| DEMetro_Z |
3.0 |
0.465 |
0.015 |
0.001 |
331.008 |
| DEMetro_Z |
4.0 |
0.462 |
0.014 |
0.001 |
479.131 |
| DEMetro_Z |
10.0 |
0.381 |
0.015 |
0.001 |
297.622 |
| DEMetro_Z |
50.0 |
0.286 |
0.014 |
0.002 |
170.418 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
Mode Transitions
Forest & Ridge Plots
Pooled
Chain
Pairwise Scatter Plots
Pooled
Chain
Varying_Tails_with_high_Correlation
(MvStudentT,
nu,
12 runs)
Pooled Chains results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
-0.117 |
0.908 |
-0.054 |
| HMC |
3.0 |
1.165 |
0.261 |
0.764 |
| HMC |
4.0 |
0.919 |
0.372 |
0.660 |
| HMC |
10.0 |
0.704 |
0.49 |
0.379 |
| HMC |
50.0 |
2.296 |
0.0347 |
1.388 |
| SMC |
2.1 |
-2.008 |
0.0588 |
-0.699 |
| SMC |
3.0 |
1.580 |
0.128 |
0.687 |
| SMC |
4.0 |
0.842 |
0.409 |
0.314 |
| SMC |
10.0 |
-2.255 |
0.0366 |
-0.766 |
| SMC |
50.0 |
0.780 |
0.444 |
0.309 |
| Metro |
2.1 |
2.258 |
0.0399 |
1.763 |
| Metro |
3.0 |
2.296 |
0.0412 |
4.197 |
| Metro |
4.0 |
4.173 |
0.00135 |
6.599 |
| Metro |
10.0 |
3.565 |
0.00414 |
6.801 |
| Metro |
50.0 |
2.972 |
0.0119 |
4.595 |
| DEMetro_Z |
2.1 |
1.483 |
0.164 |
2.269 |
| DEMetro_Z |
3.0 |
2.270 |
0.0387 |
1.711 |
| DEMetro_Z |
4.0 |
4.299 |
0.000558 |
2.843 |
| DEMetro_Z |
10.0 |
2.728 |
0.0151 |
1.859 |
| DEMetro_Z |
50.0 |
3.042 |
0.00686 |
1.657 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
-1.460
|
0.172
|
-0.421
|
| HMC_vs_DEMetro_Z |
1
|
-0.878
|
0.399
|
-0.253
|
| HMC_vs_DEMetro_Z |
2
|
-2.329
|
0.0399
|
-0.672
|
| HMC_vs_DEMetro_Z |
3
|
-2.268
|
0.0444
|
-0.655
|
| HMC_vs_DEMetro_Z |
4
|
-0.422
|
0.681
|
-0.122
|
| Metro_vs_SMC |
0
|
3.174
|
0.00886
|
0.916
|
| Metro_vs_SMC |
1
|
1.869
|
0.0885
|
0.539
|
| Metro_vs_SMC |
2
|
4.294
|
0.00127
|
1.240
|
| Metro_vs_SMC |
3
|
4.198
|
0.00149
|
1.212
|
| Metro_vs_SMC |
4
|
2.718
|
0.02
|
0.785
|
| Metro_vs_DEMetro_Z |
0
|
-0.270
|
0.792
|
-0.078
|
| Metro_vs_DEMetro_Z |
1
|
1.572
|
0.144
|
0.454
|
| Metro_vs_DEMetro_Z |
2
|
2.386
|
0.0361
|
0.689
|
| Metro_vs_DEMetro_Z |
3
|
2.445
|
0.0325
|
0.706
|
| Metro_vs_DEMetro_Z |
4
|
1.769
|
0.105
|
0.511
|
| HMC_vs_Metro |
0
|
-2.126
|
0.057
|
-0.614
|
| HMC_vs_Metro |
1
|
-1.601
|
0.138
|
-0.462
|
| HMC_vs_Metro |
2
|
-3.920
|
0.00239
|
-1.132
|
| HMC_vs_Metro |
3
|
-3.715
|
0.00341
|
-1.072
|
| HMC_vs_Metro |
4
|
-1.845
|
0.0921
|
-0.533
|
| HMC_vs_SMC |
0
|
1.578
|
0.143
|
0.455
|
| HMC_vs_SMC |
1
|
0.153
|
0.882
|
0.044
|
| HMC_vs_SMC |
2
|
0.508
|
0.622
|
0.147
|
| HMC_vs_SMC |
3
|
3.541
|
0.00462
|
1.022
|
| HMC_vs_SMC |
4
|
1.619
|
0.134
|
0.467
|
| DEMetro_Z_vs_SMC |
0
|
1.890
|
0.0854
|
0.546
|
| DEMetro_Z_vs_SMC |
1
|
1.354
|
0.203
|
0.391
|
| DEMetro_Z_vs_SMC |
2
|
3.998
|
0.0021
|
1.154
|
| DEMetro_Z_vs_SMC |
3
|
4.445
|
0.000987
|
1.283
|
| DEMetro_Z_vs_SMC |
4
|
2.729
|
0.0196
|
0.788
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.077 |
0.080 |
0.048 |
-0.054 |
| HMC |
3.0 |
0.039 |
0.025 |
0.018 |
0.764 |
| HMC |
4.0 |
0.037 |
0.026 |
0.016 |
0.660 |
| HMC |
10.0 |
0.027 |
0.022 |
0.013 |
0.379 |
| HMC |
50.0 |
0.032 |
0.015 |
0.013 |
1.388 |
| SMC |
2.1 |
0.046 |
0.080 |
0.048 |
-0.699 |
| SMC |
3.0 |
0.038 |
0.025 |
0.018 |
0.687 |
| SMC |
4.0 |
0.031 |
0.026 |
0.016 |
0.314 |
| SMC |
10.0 |
0.013 |
0.022 |
0.013 |
-0.766 |
| SMC |
50.0 |
0.019 |
0.015 |
0.013 |
0.309 |
| Metro |
2.1 |
0.165 |
0.080 |
0.048 |
1.763 |
| Metro |
3.0 |
0.101 |
0.025 |
0.018 |
4.197 |
| Metro |
4.0 |
0.134 |
0.026 |
0.016 |
6.599 |
| Metro |
10.0 |
0.110 |
0.022 |
0.013 |
6.801 |
| Metro |
50.0 |
0.073 |
0.015 |
0.013 |
4.595 |
| DEMetro_Z |
2.1 |
0.189 |
0.080 |
0.048 |
2.269 |
| DEMetro_Z |
3.0 |
0.056 |
0.025 |
0.018 |
1.711 |
| DEMetro_Z |
4.0 |
0.073 |
0.026 |
0.016 |
2.843 |
| DEMetro_Z |
10.0 |
0.046 |
0.022 |
0.013 |
1.859 |
| DEMetro_Z |
50.0 |
0.036 |
0.015 |
0.013 |
1.657 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
1.687 |
0.114 |
1.444 |
| HMC |
3.0 |
1.771 |
0.0989 |
1.565 |
| HMC |
4.0 |
2.356 |
0.0339 |
2.049 |
| HMC |
10.0 |
2.921 |
0.0118 |
2.837 |
| HMC |
50.0 |
3.231 |
0.00404 |
1.518 |
| SMC |
2.1 |
0.377 |
0.71 |
0.200 |
| SMC |
3.0 |
1.758 |
0.105 |
3.065 |
| SMC |
4.0 |
1.439 |
0.169 |
0.932 |
| SMC |
10.0 |
1.095 |
0.286 |
0.480 |
| SMC |
50.0 |
-0.212 |
0.834 |
-0.081 |
| Metro |
2.1 |
0.743 |
0.467 |
0.394 |
| Metro |
3.0 |
3.400 |
0.004 |
2.507 |
| Metro |
4.0 |
3.246 |
0.00678 |
3.911 |
| Metro |
10.0 |
1.817 |
0.0961 |
6.796 |
| Metro |
50.0 |
2.934 |
0.0117 |
2.970 |
| DEMetro_Z |
2.1 |
0.856 |
0.403 |
0.458 |
| DEMetro_Z |
3.0 |
2.541 |
0.0241 |
2.327 |
| DEMetro_Z |
4.0 |
3.262 |
0.00555 |
2.589 |
| DEMetro_Z |
10.0 |
2.848 |
0.0134 |
2.605 |
| DEMetro_Z |
50.0 |
2.261 |
0.0359 |
1.210 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
1.640
|
0.129
|
0.473
|
| HMC_vs_SMC |
1
|
-0.844
|
0.416
|
-0.244
|
| HMC_vs_SMC |
2
|
1.303
|
0.219
|
0.376
|
| HMC_vs_SMC |
3
|
2.660
|
0.0222
|
0.768
|
| HMC_vs_SMC |
4
|
4.017
|
0.00203
|
1.160
|
| Metro_vs_DEMetro_Z |
0
|
-0.595
|
0.564
|
-0.172
|
| Metro_vs_DEMetro_Z |
1
|
0.337
|
0.742
|
0.097
|
| Metro_vs_DEMetro_Z |
2
|
1.063
|
0.311
|
0.307
|
| Metro_vs_DEMetro_Z |
3
|
1.281
|
0.227
|
0.370
|
| Metro_vs_DEMetro_Z |
4
|
1.580
|
0.142
|
0.456
|
| HMC_vs_Metro |
0
|
1.400
|
0.189
|
0.404
|
| HMC_vs_Metro |
1
|
-1.204
|
0.254
|
-0.348
|
| HMC_vs_Metro |
2
|
-1.170
|
0.267
|
-0.338
|
| HMC_vs_Metro |
3
|
-1.030
|
0.325
|
-0.297
|
| HMC_vs_Metro |
4
|
-1.909
|
0.0826
|
-0.551
|
| HMC_vs_DEMetro_Z |
0
|
1.260
|
0.234
|
0.364
|
| HMC_vs_DEMetro_Z |
1
|
-1.057
|
0.313
|
-0.305
|
| HMC_vs_DEMetro_Z |
2
|
-0.511
|
0.62
|
-0.147
|
| HMC_vs_DEMetro_Z |
3
|
0.209
|
0.838
|
0.060
|
| HMC_vs_DEMetro_Z |
4
|
0.443
|
0.667
|
0.128
|
| Metro_vs_SMC |
0
|
3.695
|
0.00354
|
1.067
|
| Metro_vs_SMC |
1
|
-0.324
|
0.752
|
-0.093
|
| Metro_vs_SMC |
2
|
2.138
|
0.0558
|
0.617
|
| Metro_vs_SMC |
3
|
1.707
|
0.116
|
0.493
|
| Metro_vs_SMC |
4
|
3.065
|
0.0108
|
0.885
|
| DEMetro_Z_vs_SMC |
0
|
2.670
|
0.0218
|
0.771
|
| DEMetro_Z_vs_SMC |
1
|
-0.496
|
0.629
|
-0.143
|
| DEMetro_Z_vs_SMC |
2
|
1.834
|
0.0938
|
0.529
|
| DEMetro_Z_vs_SMC |
3
|
2.194
|
0.0506
|
0.633
|
| DEMetro_Z_vs_SMC |
4
|
2.586
|
0.0253
|
0.747
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
24.108 |
6.351 |
12.294 |
1.444 |
| HMC |
3.0 |
0.574 |
0.278 |
0.189 |
1.565 |
| HMC |
4.0 |
0.285 |
0.106 |
0.087 |
2.049 |
| HMC |
10.0 |
0.076 |
0.028 |
0.017 |
2.837 |
| HMC |
50.0 |
0.054 |
0.024 |
0.020 |
1.518 |
| SMC |
2.1 |
8.812 |
6.351 |
12.294 |
0.200 |
| SMC |
3.0 |
0.857 |
0.278 |
0.189 |
3.065 |
| SMC |
4.0 |
0.187 |
0.106 |
0.087 |
0.932 |
| SMC |
10.0 |
0.036 |
0.028 |
0.017 |
0.480 |
| SMC |
50.0 |
0.022 |
0.024 |
0.020 |
-0.081 |
| Metro |
2.1 |
11.195 |
6.351 |
12.294 |
0.394 |
| Metro |
3.0 |
0.752 |
0.278 |
0.189 |
2.507 |
| Metro |
4.0 |
0.447 |
0.106 |
0.087 |
3.911 |
| Metro |
10.0 |
0.143 |
0.028 |
0.017 |
6.796 |
| Metro |
50.0 |
0.082 |
0.024 |
0.020 |
2.970 |
| DEMetro_Z |
2.1 |
11.979 |
6.351 |
12.294 |
0.458 |
| DEMetro_Z |
3.0 |
0.718 |
0.278 |
0.189 |
2.327 |
| DEMetro_Z |
4.0 |
0.332 |
0.106 |
0.087 |
2.589 |
| DEMetro_Z |
10.0 |
0.072 |
0.028 |
0.017 |
2.605 |
| DEMetro_Z |
50.0 |
0.048 |
0.024 |
0.020 |
1.210 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
2.240 |
0.0454 |
3.786 |
| HMC |
3.0 |
4.572 |
0.000353 |
3.232 |
| HMC |
4.0 |
3.334 |
0.00444 |
2.350 |
| HMC |
10.0 |
3.236 |
0.00462 |
1.832 |
| HMC |
50.0 |
3.658 |
0.00211 |
2.383 |
| SMC |
2.1 |
-0.036 |
0.972 |
-0.016 |
| SMC |
3.0 |
1.479 |
0.158 |
0.956 |
| SMC |
4.0 |
0.416 |
0.682 |
0.144 |
| SMC |
10.0 |
-1.941 |
0.0657 |
-0.725 |
| SMC |
50.0 |
0.568 |
0.576 |
0.226 |
| Metro |
2.1 |
6.918 |
5.82e-06 |
5.307 |
| Metro |
3.0 |
6.544 |
3.56e-05 |
14.676 |
| Metro |
4.0 |
5.005 |
0.000355 |
10.321 |
| Metro |
10.0 |
4.000 |
0.00202 |
12.632 |
| Metro |
50.0 |
3.568 |
0.00421 |
8.346 |
| DEMetro_Z |
2.1 |
3.100 |
0.00949 |
5.280 |
| DEMetro_Z |
3.0 |
5.643 |
0.00011 |
8.023 |
| DEMetro_Z |
4.0 |
5.899 |
4.47e-05 |
5.278 |
| DEMetro_Z |
10.0 |
4.319 |
0.000713 |
3.601 |
| DEMetro_Z |
50.0 |
6.136 |
7.92e-06 |
3.374 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
0.013
|
0.99
|
0.004
|
| Metro_vs_DEMetro_Z |
1
|
3.329
|
0.00672
|
0.961
|
| Metro_vs_DEMetro_Z |
2
|
2.159
|
0.0538
|
0.623
|
| Metro_vs_DEMetro_Z |
3
|
2.991
|
0.0123
|
0.863
|
| Metro_vs_DEMetro_Z |
4
|
1.970
|
0.0745
|
0.569
|
| DEMetro_Z_vs_SMC |
0
|
3.021
|
0.0116
|
0.872
|
| DEMetro_Z_vs_SMC |
1
|
4.903
|
0.00047
|
1.415
|
| DEMetro_Z_vs_SMC |
2
|
6.232
|
6.42e-05
|
1.799
|
| DEMetro_Z_vs_SMC |
3
|
5.088
|
0.000351
|
1.469
|
| DEMetro_Z_vs_SMC |
4
|
5.843
|
0.000112
|
1.687
|
| HMC_vs_DEMetro_Z |
0
|
-0.551
|
0.593
|
-0.159
|
| HMC_vs_DEMetro_Z |
1
|
-3.547
|
0.00458
|
-1.024
|
| HMC_vs_DEMetro_Z |
2
|
-3.742
|
0.00325
|
-1.080
|
| HMC_vs_DEMetro_Z |
3
|
-2.172
|
0.0526
|
-0.627
|
| HMC_vs_DEMetro_Z |
4
|
-1.548
|
0.15
|
-0.447
|
| HMC_vs_Metro |
0
|
-0.812
|
0.434
|
-0.235
|
| HMC_vs_Metro |
1
|
-4.650
|
0.000705
|
-1.342
|
| HMC_vs_Metro |
2
|
-3.778
|
0.00306
|
-1.090
|
| HMC_vs_Metro |
3
|
-3.558
|
0.00448
|
-1.027
|
| HMC_vs_Metro |
4
|
-2.535
|
0.0277
|
-0.732
|
| HMC_vs_SMC |
0
|
2.206
|
0.0496
|
0.637
|
| HMC_vs_SMC |
1
|
3.776
|
0.00307
|
1.090
|
| HMC_vs_SMC |
2
|
3.573
|
0.00437
|
1.031
|
| HMC_vs_SMC |
3
|
5.121
|
0.000333
|
1.478
|
| HMC_vs_SMC |
4
|
3.050
|
0.011
|
0.881
|
| Metro_vs_SMC |
0
|
10.833
|
3.3e-07
|
3.127
|
| Metro_vs_SMC |
1
|
6.271
|
6.08e-05
|
1.810
|
| Metro_vs_SMC |
2
|
4.925
|
0.000453
|
1.422
|
| Metro_vs_SMC |
3
|
4.285
|
0.00129
|
1.237
|
| Metro_vs_SMC |
4
|
3.380
|
0.00614
|
0.976
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.273 |
0.119 |
0.041 |
3.786 |
| HMC |
3.0 |
0.086 |
0.058 |
0.008 |
3.232 |
| HMC |
4.0 |
0.073 |
0.046 |
0.012 |
2.350 |
| HMC |
10.0 |
0.045 |
0.032 |
0.007 |
1.832 |
| HMC |
50.0 |
0.042 |
0.024 |
0.007 |
2.383 |
| SMC |
2.1 |
0.118 |
0.119 |
0.041 |
-0.016 |
| SMC |
3.0 |
0.067 |
0.058 |
0.008 |
0.956 |
| SMC |
4.0 |
0.048 |
0.046 |
0.012 |
0.144 |
| SMC |
10.0 |
0.027 |
0.032 |
0.007 |
-0.725 |
| SMC |
50.0 |
0.026 |
0.024 |
0.007 |
0.226 |
| Metro |
2.1 |
0.335 |
0.119 |
0.041 |
5.307 |
| Metro |
3.0 |
0.183 |
0.058 |
0.008 |
14.676 |
| Metro |
4.0 |
0.166 |
0.046 |
0.012 |
10.321 |
| Metro |
10.0 |
0.120 |
0.032 |
0.007 |
12.632 |
| Metro |
50.0 |
0.086 |
0.024 |
0.007 |
8.346 |
| DEMetro_Z |
2.1 |
0.334 |
0.119 |
0.041 |
5.280 |
| DEMetro_Z |
3.0 |
0.126 |
0.058 |
0.008 |
8.023 |
| DEMetro_Z |
4.0 |
0.107 |
0.046 |
0.012 |
5.278 |
| DEMetro_Z |
10.0 |
0.057 |
0.032 |
0.007 |
3.601 |
| DEMetro_Z |
50.0 |
0.049 |
0.024 |
0.007 |
3.374 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
4.061 |
0.000633 |
2.061 |
| HMC |
3.0 |
3.340 |
0.00356 |
1.828 |
| HMC |
4.0 |
2.775 |
0.0129 |
1.656 |
| HMC |
10.0 |
2.637 |
0.0167 |
1.477 |
| HMC |
50.0 |
4.515 |
0.000186 |
2.052 |
| SMC |
2.1 |
1.034 |
0.318 |
0.793 |
| SMC |
3.0 |
0.336 |
0.74 |
0.172 |
| SMC |
4.0 |
-0.697 |
0.494 |
-0.260 |
| SMC |
10.0 |
-1.794 |
0.0869 |
-0.691 |
| SMC |
50.0 |
0.442 |
0.663 |
0.166 |
| Metro |
2.1 |
6.931 |
1.54e-05 |
9.333 |
| Metro |
3.0 |
6.509 |
2.8e-05 |
8.660 |
| Metro |
4.0 |
3.442 |
0.00511 |
6.105 |
| Metro |
10.0 |
4.266 |
0.00113 |
6.475 |
| Metro |
50.0 |
4.384 |
0.00097 |
7.972 |
| DEMetro_Z |
2.1 |
5.284 |
0.00017 |
6.093 |
| DEMetro_Z |
3.0 |
6.831 |
3.46e-06 |
4.300 |
| DEMetro_Z |
4.0 |
3.828 |
0.00188 |
3.246 |
| DEMetro_Z |
10.0 |
3.106 |
0.00809 |
2.845 |
| DEMetro_Z |
50.0 |
4.027 |
0.00116 |
3.086 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
3.723
|
0.00337
|
1.075
|
| DEMetro_Z_vs_SMC |
1
|
5.549
|
0.000173
|
1.602
|
| DEMetro_Z_vs_SMC |
2
|
4.069
|
0.00186
|
1.175
|
| DEMetro_Z_vs_SMC |
3
|
3.644
|
0.00386
|
1.052
|
| DEMetro_Z_vs_SMC |
4
|
3.786
|
0.00302
|
1.093
|
| HMC_vs_Metro |
0
|
-5.756
|
0.000127
|
-1.662
|
| HMC_vs_Metro |
1
|
-5.190
|
0.000299
|
-1.498
|
| HMC_vs_Metro |
2
|
-2.399
|
0.0353
|
-0.692
|
| HMC_vs_Metro |
3
|
-3.586
|
0.00427
|
-1.035
|
| HMC_vs_Metro |
4
|
-3.436
|
0.00556
|
-0.992
|
| Metro_vs_DEMetro_Z |
0
|
1.828
|
0.0948
|
0.528
|
| Metro_vs_DEMetro_Z |
1
|
3.022
|
0.0116
|
0.872
|
| Metro_vs_DEMetro_Z |
2
|
1.477
|
0.168
|
0.426
|
| Metro_vs_DEMetro_Z |
3
|
2.135
|
0.0561
|
0.616
|
| Metro_vs_DEMetro_Z |
4
|
2.250
|
0.0459
|
0.649
|
| HMC_vs_SMC |
0
|
1.399
|
0.189
|
0.404
|
| HMC_vs_SMC |
1
|
3.322
|
0.0068
|
0.959
|
| HMC_vs_SMC |
2
|
4.566
|
0.000808
|
1.318
|
| HMC_vs_SMC |
3
|
3.995
|
0.0021
|
1.153
|
| HMC_vs_SMC |
4
|
4.023
|
0.00201
|
1.161
|
| Metro_vs_SMC |
0
|
7.614
|
1.04e-05
|
2.198
|
| Metro_vs_SMC |
1
|
7.769
|
8.62e-06
|
2.243
|
| Metro_vs_SMC |
2
|
3.500
|
0.00497
|
1.010
|
| Metro_vs_SMC |
3
|
4.810
|
0.000545
|
1.388
|
| Metro_vs_SMC |
4
|
4.339
|
0.00118
|
1.253
|
| HMC_vs_DEMetro_Z |
0
|
-3.153
|
0.00919
|
-0.910
|
| HMC_vs_DEMetro_Z |
1
|
-3.332
|
0.00669
|
-0.962
|
| HMC_vs_DEMetro_Z |
2
|
-1.941
|
0.0783
|
-0.560
|
| HMC_vs_DEMetro_Z |
3
|
-1.375
|
0.196
|
-0.397
|
| HMC_vs_DEMetro_Z |
4
|
-1.313
|
0.216
|
-0.379
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.026 |
0.015 |
0.005 |
2.061 |
| HMC |
3.0 |
0.022 |
0.014 |
0.004 |
1.828 |
| HMC |
4.0 |
0.024 |
0.015 |
0.005 |
1.656 |
| HMC |
10.0 |
0.021 |
0.014 |
0.004 |
1.477 |
| HMC |
50.0 |
0.021 |
0.012 |
0.004 |
2.052 |
| SMC |
2.1 |
0.019 |
0.015 |
0.005 |
0.793 |
| SMC |
3.0 |
0.015 |
0.014 |
0.004 |
0.172 |
| SMC |
4.0 |
0.014 |
0.015 |
0.005 |
-0.260 |
| SMC |
10.0 |
0.011 |
0.014 |
0.004 |
-0.691 |
| SMC |
50.0 |
0.013 |
0.012 |
0.004 |
0.166 |
| Metro |
2.1 |
0.064 |
0.015 |
0.005 |
9.333 |
| Metro |
3.0 |
0.049 |
0.014 |
0.004 |
8.660 |
| Metro |
4.0 |
0.048 |
0.015 |
0.005 |
6.105 |
| Metro |
10.0 |
0.042 |
0.014 |
0.004 |
6.475 |
| Metro |
50.0 |
0.046 |
0.012 |
0.004 |
7.972 |
| DEMetro_Z |
2.1 |
0.047 |
0.015 |
0.005 |
6.093 |
| DEMetro_Z |
3.0 |
0.032 |
0.014 |
0.004 |
4.300 |
| DEMetro_Z |
4.0 |
0.033 |
0.015 |
0.005 |
3.246 |
| DEMetro_Z |
10.0 |
0.027 |
0.014 |
0.004 |
2.845 |
| DEMetro_Z |
50.0 |
0.025 |
0.012 |
0.004 |
3.086 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
R Hat (scatter)
Mode Transitions
One Chain results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
-0.186 |
0.854 |
-0.086 |
| HMC |
3.0 |
1.477 |
0.16 |
1.075 |
| HMC |
4.0 |
2.606 |
0.0193 |
1.753 |
| HMC |
10.0 |
0.390 |
0.702 |
0.235 |
| HMC |
50.0 |
1.930 |
0.0716 |
1.265 |
| SMC |
2.1 |
-0.953 |
0.352 |
-0.334 |
| SMC |
3.0 |
1.111 |
0.281 |
0.601 |
| SMC |
4.0 |
-1.439 |
0.169 |
-0.466 |
| SMC |
10.0 |
-0.737 |
0.469 |
-0.280 |
| SMC |
50.0 |
0.111 |
0.912 |
0.041 |
| Metro |
2.1 |
2.660 |
0.0204 |
3.229 |
| Metro |
3.0 |
3.787 |
0.00265 |
5.662 |
| Metro |
4.0 |
3.780 |
0.0024 |
4.134 |
| Metro |
10.0 |
2.979 |
0.0114 |
3.910 |
| Metro |
50.0 |
5.154 |
0.000227 |
6.542 |
| DEMetro_Z |
2.1 |
1.901 |
0.0761 |
1.307 |
| DEMetro_Z |
3.0 |
3.360 |
0.00445 |
2.567 |
| DEMetro_Z |
4.0 |
2.575 |
0.0221 |
2.158 |
| DEMetro_Z |
10.0 |
2.717 |
0.0127 |
1.188 |
| DEMetro_Z |
50.0 |
1.594 |
0.132 |
1.192 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
-1.785
|
0.102
|
-0.515
|
| HMC_vs_DEMetro_Z |
1
|
-1.274
|
0.229
|
-0.368
|
| HMC_vs_DEMetro_Z |
2
|
-0.383
|
0.709
|
-0.110
|
| HMC_vs_DEMetro_Z |
3
|
-1.836
|
0.0936
|
-0.530
|
| HMC_vs_DEMetro_Z |
4
|
0.074
|
0.942
|
0.021
|
| Metro_vs_SMC |
0
|
2.972
|
0.0127
|
0.858
|
| Metro_vs_SMC |
1
|
2.927
|
0.0138
|
0.845
|
| Metro_vs_SMC |
2
|
4.579
|
0.000792
|
1.322
|
| Metro_vs_SMC |
3
|
3.558
|
0.00449
|
1.027
|
| Metro_vs_SMC |
4
|
5.543
|
0.000174
|
1.600
|
| Metro_vs_DEMetro_Z |
0
|
1.689
|
0.119
|
0.488
|
| Metro_vs_DEMetro_Z |
1
|
2.240
|
0.0467
|
0.647
|
| Metro_vs_DEMetro_Z |
2
|
1.301
|
0.22
|
0.376
|
| Metro_vs_DEMetro_Z |
3
|
2.022
|
0.0681
|
0.584
|
| Metro_vs_DEMetro_Z |
4
|
3.382
|
0.00612
|
0.976
|
| HMC_vs_Metro |
0
|
-2.434
|
0.0332
|
-0.703
|
| HMC_vs_Metro |
1
|
-2.676
|
0.0216
|
-0.773
|
| HMC_vs_Metro |
2
|
-1.858
|
0.0901
|
-0.536
|
| HMC_vs_Metro |
3
|
-2.626
|
0.0236
|
-0.758
|
| HMC_vs_Metro |
4
|
-4.010
|
0.00205
|
-1.157
|
| HMC_vs_SMC |
0
|
0.797
|
0.442
|
0.230
|
| HMC_vs_SMC |
1
|
0.504
|
0.624
|
0.145
|
| HMC_vs_SMC |
2
|
3.710
|
0.00344
|
1.071
|
| HMC_vs_SMC |
3
|
0.932
|
0.372
|
0.269
|
| HMC_vs_SMC |
4
|
2.236
|
0.047
|
0.646
|
| DEMetro_Z_vs_SMC |
0
|
2.363
|
0.0376
|
0.682
|
| DEMetro_Z_vs_SMC |
1
|
2.485
|
0.0303
|
0.717
|
| DEMetro_Z_vs_SMC |
2
|
3.151
|
0.00922
|
0.910
|
| DEMetro_Z_vs_SMC |
3
|
3.073
|
0.0106
|
0.887
|
| DEMetro_Z_vs_SMC |
4
|
1.595
|
0.139
|
0.460
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.076 |
0.080 |
0.048 |
-0.086 |
| HMC |
3.0 |
0.045 |
0.025 |
0.018 |
1.075 |
| HMC |
4.0 |
0.055 |
0.026 |
0.016 |
1.753 |
| HMC |
10.0 |
0.025 |
0.022 |
0.013 |
0.235 |
| HMC |
50.0 |
0.031 |
0.015 |
0.013 |
1.265 |
| SMC |
2.1 |
0.064 |
0.080 |
0.048 |
-0.334 |
| SMC |
3.0 |
0.036 |
0.025 |
0.018 |
0.601 |
| SMC |
4.0 |
0.018 |
0.026 |
0.016 |
-0.466 |
| SMC |
10.0 |
0.019 |
0.022 |
0.013 |
-0.280 |
| SMC |
50.0 |
0.015 |
0.015 |
0.013 |
0.041 |
| Metro |
2.1 |
0.235 |
0.080 |
0.048 |
3.229 |
| Metro |
3.0 |
0.128 |
0.025 |
0.018 |
5.662 |
| Metro |
4.0 |
0.094 |
0.026 |
0.016 |
4.134 |
| Metro |
10.0 |
0.073 |
0.022 |
0.013 |
3.910 |
| Metro |
50.0 |
0.097 |
0.015 |
0.013 |
6.542 |
| DEMetro_Z |
2.1 |
0.143 |
0.080 |
0.048 |
1.307 |
| DEMetro_Z |
3.0 |
0.072 |
0.025 |
0.018 |
2.567 |
| DEMetro_Z |
4.0 |
0.061 |
0.026 |
0.016 |
2.158 |
| DEMetro_Z |
10.0 |
0.038 |
0.022 |
0.013 |
1.188 |
| DEMetro_Z |
50.0 |
0.030 |
0.015 |
0.013 |
1.192 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
0.510 |
0.616 |
0.264 |
| HMC |
3.0 |
1.664 |
0.12 |
1.764 |
| HMC |
4.0 |
1.272 |
0.221 |
0.814 |
| HMC |
10.0 |
2.298 |
0.0388 |
2.301 |
| HMC |
50.0 |
2.606 |
0.0163 |
1.151 |
| SMC |
2.1 |
0.456 |
0.653 |
0.240 |
| SMC |
3.0 |
1.153 |
0.263 |
0.599 |
| SMC |
4.0 |
0.543 |
0.593 |
0.221 |
| SMC |
10.0 |
0.534 |
0.599 |
0.270 |
| SMC |
50.0 |
1.614 |
0.121 |
0.648 |
| Metro |
2.1 |
0.668 |
0.512 |
0.344 |
| Metro |
3.0 |
1.857 |
0.0865 |
1.953 |
| Metro |
4.0 |
3.053 |
0.0097 |
3.611 |
| Metro |
10.0 |
4.473 |
0.000797 |
6.963 |
| Metro |
50.0 |
3.492 |
0.00428 |
4.238 |
| DEMetro_Z |
2.1 |
0.647 |
0.525 |
0.348 |
| DEMetro_Z |
3.0 |
3.036 |
0.0091 |
2.645 |
| DEMetro_Z |
4.0 |
3.733 |
0.00124 |
1.741 |
| DEMetro_Z |
10.0 |
2.938 |
0.0112 |
2.692 |
| DEMetro_Z |
50.0 |
1.936 |
0.071 |
1.294 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
0.638
|
0.536
|
0.184
|
| HMC_vs_SMC |
1
|
1.052
|
0.315
|
0.304
|
| HMC_vs_SMC |
2
|
1.009
|
0.335
|
0.291
|
| HMC_vs_SMC |
3
|
1.854
|
0.0907
|
0.535
|
| HMC_vs_SMC |
4
|
1.233
|
0.243
|
0.356
|
| Metro_vs_DEMetro_Z |
0
|
-0.060
|
0.953
|
-0.017
|
| Metro_vs_DEMetro_Z |
1
|
-0.717
|
0.488
|
-0.207
|
| Metro_vs_DEMetro_Z |
2
|
1.803
|
0.0988
|
0.521
|
| Metro_vs_DEMetro_Z |
3
|
2.663
|
0.0221
|
0.769
|
| Metro_vs_DEMetro_Z |
4
|
2.071
|
0.0627
|
0.598
|
| HMC_vs_Metro |
0
|
-1.038
|
0.322
|
-0.300
|
| HMC_vs_Metro |
1
|
-0.154
|
0.88
|
-0.045
|
| HMC_vs_Metro |
2
|
-2.461
|
0.0316
|
-0.710
|
| HMC_vs_Metro |
3
|
-2.375
|
0.0368
|
-0.686
|
| HMC_vs_Metro |
4
|
-2.968
|
0.0128
|
-0.857
|
| HMC_vs_DEMetro_Z |
0
|
-2.352
|
0.0384
|
-0.679
|
| HMC_vs_DEMetro_Z |
1
|
-0.933
|
0.371
|
-0.269
|
| HMC_vs_DEMetro_Z |
2
|
-1.526
|
0.155
|
-0.441
|
| HMC_vs_DEMetro_Z |
3
|
-0.337
|
0.743
|
-0.097
|
| HMC_vs_DEMetro_Z |
4
|
-0.232
|
0.821
|
-0.067
|
| Metro_vs_SMC |
0
|
1.829
|
0.0947
|
0.528
|
| Metro_vs_SMC |
1
|
1.317
|
0.215
|
0.380
|
| Metro_vs_SMC |
2
|
2.806
|
0.0171
|
0.810
|
| Metro_vs_SMC |
3
|
4.984
|
0.000413
|
1.439
|
| Metro_vs_SMC |
4
|
3.614
|
0.00407
|
1.043
|
| DEMetro_Z_vs_SMC |
0
|
3.111
|
0.00991
|
0.898
|
| DEMetro_Z_vs_SMC |
1
|
2.786
|
0.0177
|
0.804
|
| DEMetro_Z_vs_SMC |
2
|
3.622
|
0.00401
|
1.046
|
| DEMetro_Z_vs_SMC |
3
|
2.571
|
0.026
|
0.742
|
| DEMetro_Z_vs_SMC |
4
|
0.920
|
0.377
|
0.266
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
9.598 |
6.351 |
12.294 |
0.264 |
| HMC |
3.0 |
0.611 |
0.278 |
0.189 |
1.764 |
| HMC |
4.0 |
0.177 |
0.106 |
0.087 |
0.814 |
| HMC |
10.0 |
0.067 |
0.028 |
0.017 |
2.301 |
| HMC |
50.0 |
0.046 |
0.024 |
0.020 |
1.151 |
| SMC |
2.1 |
9.296 |
6.351 |
12.294 |
0.240 |
| SMC |
3.0 |
0.391 |
0.278 |
0.189 |
0.599 |
| SMC |
4.0 |
0.125 |
0.106 |
0.087 |
0.221 |
| SMC |
10.0 |
0.032 |
0.028 |
0.017 |
0.270 |
| SMC |
50.0 |
0.037 |
0.024 |
0.020 |
0.648 |
| Metro |
2.1 |
10.576 |
6.351 |
12.294 |
0.344 |
| Metro |
3.0 |
0.647 |
0.278 |
0.189 |
1.953 |
| Metro |
4.0 |
0.421 |
0.106 |
0.087 |
3.611 |
| Metro |
10.0 |
0.146 |
0.028 |
0.017 |
6.963 |
| Metro |
50.0 |
0.107 |
0.024 |
0.020 |
4.238 |
| DEMetro_Z |
2.1 |
10.634 |
6.351 |
12.294 |
0.348 |
| DEMetro_Z |
3.0 |
0.778 |
0.278 |
0.189 |
2.645 |
| DEMetro_Z |
4.0 |
0.258 |
0.106 |
0.087 |
1.741 |
| DEMetro_Z |
10.0 |
0.073 |
0.028 |
0.017 |
2.692 |
| DEMetro_Z |
50.0 |
0.049 |
0.024 |
0.020 |
1.294 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
1.694 |
0.105 |
0.815 |
| HMC |
3.0 |
3.159 |
0.00746 |
3.060 |
| HMC |
4.0 |
3.986 |
0.00113 |
2.757 |
| HMC |
10.0 |
1.439 |
0.172 |
1.166 |
| HMC |
50.0 |
3.727 |
0.00181 |
2.407 |
| SMC |
2.1 |
0.187 |
0.853 |
0.081 |
| SMC |
3.0 |
0.911 |
0.375 |
0.563 |
| SMC |
4.0 |
-1.196 |
0.247 |
-0.404 |
| SMC |
10.0 |
-0.892 |
0.382 |
-0.396 |
| SMC |
50.0 |
0.671 |
0.51 |
0.238 |
| Metro |
2.1 |
5.814 |
6.37e-05 |
6.045 |
| Metro |
3.0 |
7.490 |
9.73e-06 |
15.572 |
| Metro |
4.0 |
6.099 |
4.76e-05 |
7.365 |
| Metro |
10.0 |
6.278 |
3.97e-05 |
8.401 |
| Metro |
50.0 |
8.128 |
3.1e-06 |
10.949 |
| DEMetro_Z |
2.1 |
4.239 |
0.000855 |
3.636 |
| DEMetro_Z |
3.0 |
8.574 |
1.12e-06 |
8.818 |
| DEMetro_Z |
4.0 |
4.769 |
0.000304 |
3.986 |
| DEMetro_Z |
10.0 |
5.487 |
2.97e-05 |
2.980 |
| DEMetro_Z |
50.0 |
4.244 |
0.000808 |
3.464 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
1.913
|
0.0821
|
0.552
|
| Metro_vs_DEMetro_Z |
1
|
2.962
|
0.0129
|
0.855
|
| Metro_vs_DEMetro_Z |
2
|
1.865
|
0.089
|
0.538
|
| Metro_vs_DEMetro_Z |
3
|
4.007
|
0.00206
|
1.157
|
| Metro_vs_DEMetro_Z |
4
|
4.398
|
0.00107
|
1.270
|
| DEMetro_Z_vs_SMC |
0
|
4.151
|
0.00161
|
1.198
|
| DEMetro_Z_vs_SMC |
1
|
8.360
|
4.29e-06
|
2.413
|
| DEMetro_Z_vs_SMC |
2
|
5.550
|
0.000173
|
1.602
|
| DEMetro_Z_vs_SMC |
3
|
5.483
|
0.000191
|
1.583
|
| DEMetro_Z_vs_SMC |
4
|
4.015
|
0.00203
|
1.159
|
| HMC_vs_DEMetro_Z |
0
|
-3.012
|
0.0118
|
-0.869
|
| HMC_vs_DEMetro_Z |
1
|
-5.669
|
0.000145
|
-1.636
|
| HMC_vs_DEMetro_Z |
2
|
-1.088
|
0.3
|
-0.314
|
| HMC_vs_DEMetro_Z |
3
|
-2.290
|
0.0428
|
-0.661
|
| HMC_vs_DEMetro_Z |
4
|
-1.218
|
0.249
|
-0.352
|
| HMC_vs_Metro |
0
|
-4.985
|
0.000412
|
-1.439
|
| HMC_vs_Metro |
1
|
-4.914
|
0.000461
|
-1.419
|
| HMC_vs_Metro |
2
|
-3.649
|
0.00383
|
-1.053
|
| HMC_vs_Metro |
3
|
-4.315
|
0.00122
|
-1.246
|
| HMC_vs_Metro |
4
|
-6.634
|
3.69e-05
|
-1.915
|
| HMC_vs_SMC |
0
|
3.172
|
0.00889
|
0.916
|
| HMC_vs_SMC |
1
|
2.100
|
0.0596
|
0.606
|
| HMC_vs_SMC |
2
|
4.280
|
0.0013
|
1.235
|
| HMC_vs_SMC |
3
|
1.710
|
0.115
|
0.494
|
| HMC_vs_SMC |
4
|
3.931
|
0.00235
|
1.135
|
| Metro_vs_SMC |
0
|
5.862
|
0.000109
|
1.692
|
| Metro_vs_SMC |
1
|
6.718
|
3.3e-05
|
1.939
|
| Metro_vs_SMC |
2
|
6.470
|
4.62e-05
|
1.868
|
| Metro_vs_SMC |
3
|
7.558
|
1.12e-05
|
2.182
|
| Metro_vs_SMC |
4
|
8.726
|
2.83e-06
|
2.519
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.152 |
0.119 |
0.041 |
0.815 |
| HMC |
3.0 |
0.084 |
0.058 |
0.008 |
3.060 |
| HMC |
4.0 |
0.078 |
0.046 |
0.012 |
2.757 |
| HMC |
10.0 |
0.040 |
0.032 |
0.007 |
1.166 |
| HMC |
50.0 |
0.042 |
0.024 |
0.007 |
2.407 |
| SMC |
2.1 |
0.122 |
0.119 |
0.041 |
0.081 |
| SMC |
3.0 |
0.063 |
0.058 |
0.008 |
0.563 |
| SMC |
4.0 |
0.041 |
0.046 |
0.012 |
-0.404 |
| SMC |
10.0 |
0.029 |
0.032 |
0.007 |
-0.396 |
| SMC |
50.0 |
0.026 |
0.024 |
0.007 |
0.238 |
| Metro |
2.1 |
0.365 |
0.119 |
0.041 |
6.045 |
| Metro |
3.0 |
0.190 |
0.058 |
0.008 |
15.572 |
| Metro |
4.0 |
0.132 |
0.046 |
0.012 |
7.365 |
| Metro |
10.0 |
0.091 |
0.032 |
0.007 |
8.401 |
| Metro |
50.0 |
0.105 |
0.024 |
0.007 |
10.949 |
| DEMetro_Z |
2.1 |
0.267 |
0.119 |
0.041 |
3.636 |
| DEMetro_Z |
3.0 |
0.133 |
0.058 |
0.008 |
8.818 |
| DEMetro_Z |
4.0 |
0.092 |
0.046 |
0.012 |
3.986 |
| DEMetro_Z |
10.0 |
0.053 |
0.032 |
0.007 |
2.980 |
| DEMetro_Z |
50.0 |
0.050 |
0.024 |
0.007 |
3.464 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
1.773 |
0.0942 |
1.075 |
| HMC |
3.0 |
1.656 |
0.115 |
0.948 |
| HMC |
4.0 |
3.023 |
0.00739 |
1.727 |
| HMC |
10.0 |
1.240 |
0.231 |
0.677 |
| HMC |
50.0 |
4.307 |
0.000406 |
2.355 |
| SMC |
2.1 |
0.359 |
0.723 |
0.126 |
| SMC |
3.0 |
0.157 |
0.877 |
0.086 |
| SMC |
4.0 |
-1.383 |
0.181 |
-0.514 |
| SMC |
10.0 |
-0.811 |
0.426 |
-0.332 |
| SMC |
50.0 |
0.689 |
0.499 |
0.241 |
| Metro |
2.1 |
6.927 |
1.71e-05 |
10.474 |
| Metro |
3.0 |
7.270 |
9.59e-06 |
9.774 |
| Metro |
4.0 |
5.740 |
5.13e-05 |
4.751 |
| Metro |
10.0 |
8.393 |
8.66e-07 |
7.161 |
| Metro |
50.0 |
7.914 |
4.2e-06 |
10.936 |
| DEMetro_Z |
2.1 |
3.263 |
0.00706 |
5.650 |
| DEMetro_Z |
3.0 |
5.176 |
0.000182 |
5.249 |
| DEMetro_Z |
4.0 |
3.280 |
0.00531 |
2.564 |
| DEMetro_Z |
10.0 |
4.488 |
0.000357 |
2.869 |
| DEMetro_Z |
50.0 |
3.831 |
0.00177 |
3.027 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
3.269
|
0.00748
|
0.944
|
| DEMetro_Z_vs_SMC |
1
|
5.341
|
0.000237
|
1.542
|
| DEMetro_Z_vs_SMC |
2
|
4.331
|
0.00119
|
1.250
|
| DEMetro_Z_vs_SMC |
3
|
4.615
|
0.000747
|
1.332
|
| DEMetro_Z_vs_SMC |
4
|
3.489
|
0.00506
|
1.007
|
| HMC_vs_Metro |
0
|
-5.726
|
0.000133
|
-1.653
|
| HMC_vs_Metro |
1
|
-6.977
|
2.34e-05
|
-2.014
|
| HMC_vs_Metro |
2
|
-3.442
|
0.00551
|
-0.993
|
| HMC_vs_Metro |
3
|
-6.977
|
2.34e-05
|
-2.014
|
| HMC_vs_Metro |
4
|
-6.152
|
7.19e-05
|
-1.776
|
| Metro_vs_DEMetro_Z |
0
|
2.256
|
0.0454
|
0.651
|
| Metro_vs_DEMetro_Z |
1
|
2.804
|
0.0172
|
0.809
|
| Metro_vs_DEMetro_Z |
2
|
1.540
|
0.152
|
0.444
|
| Metro_vs_DEMetro_Z |
3
|
5.453
|
0.0002
|
1.574
|
| Metro_vs_DEMetro_Z |
4
|
4.622
|
0.000739
|
1.334
|
| HMC_vs_SMC |
0
|
2.233
|
0.0473
|
0.645
|
| HMC_vs_SMC |
1
|
1.308
|
0.218
|
0.378
|
| HMC_vs_SMC |
2
|
3.620
|
0.00402
|
1.045
|
| HMC_vs_SMC |
3
|
1.562
|
0.147
|
0.451
|
| HMC_vs_SMC |
4
|
4.438
|
0.000999
|
1.281
|
| Metro_vs_SMC |
0
|
6.729
|
3.25e-05
|
1.942
|
| Metro_vs_SMC |
1
|
7.769
|
8.63e-06
|
2.243
|
| Metro_vs_SMC |
2
|
6.202
|
6.7e-05
|
1.790
|
| Metro_vs_SMC |
3
|
9.380
|
1.4e-06
|
2.708
|
| Metro_vs_SMC |
4
|
8.314
|
4.52e-06
|
2.400
|
| HMC_vs_DEMetro_Z |
0
|
-2.472
|
0.031
|
-0.713
|
| HMC_vs_DEMetro_Z |
1
|
-4.431
|
0.00101
|
-1.279
|
| HMC_vs_DEMetro_Z |
2
|
-0.900
|
0.388
|
-0.260
|
| HMC_vs_DEMetro_Z |
3
|
-3.611
|
0.00409
|
-1.043
|
| HMC_vs_DEMetro_Z |
4
|
-1.033
|
0.324
|
-0.298
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.021 |
0.015 |
0.005 |
1.075 |
| HMC |
3.0 |
0.018 |
0.014 |
0.004 |
0.948 |
| HMC |
4.0 |
0.025 |
0.015 |
0.005 |
1.727 |
| HMC |
10.0 |
0.017 |
0.014 |
0.004 |
0.677 |
| HMC |
50.0 |
0.022 |
0.012 |
0.004 |
2.355 |
| SMC |
2.1 |
0.016 |
0.015 |
0.005 |
0.126 |
| SMC |
3.0 |
0.014 |
0.014 |
0.004 |
0.086 |
| SMC |
4.0 |
0.013 |
0.015 |
0.005 |
-0.514 |
| SMC |
10.0 |
0.013 |
0.014 |
0.004 |
-0.332 |
| SMC |
50.0 |
0.013 |
0.012 |
0.004 |
0.241 |
| Metro |
2.1 |
0.070 |
0.015 |
0.005 |
10.474 |
| Metro |
3.0 |
0.054 |
0.014 |
0.004 |
9.774 |
| Metro |
4.0 |
0.041 |
0.015 |
0.005 |
4.751 |
| Metro |
10.0 |
0.045 |
0.014 |
0.004 |
7.161 |
| Metro |
50.0 |
0.059 |
0.012 |
0.004 |
10.936 |
| DEMetro_Z |
2.1 |
0.045 |
0.015 |
0.005 |
5.650 |
| DEMetro_Z |
3.0 |
0.036 |
0.014 |
0.004 |
5.249 |
| DEMetro_Z |
4.0 |
0.029 |
0.015 |
0.005 |
2.564 |
| DEMetro_Z |
10.0 |
0.027 |
0.014 |
0.004 |
2.869 |
| DEMetro_Z |
50.0 |
0.025 |
0.012 |
0.004 |
3.027 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
Mode Transitions
KDE + Init Plots
Forest & Ridge Plots
Pooled
Chain
Pairwise Scatter Plots
Pooled
Chain
Vary_Tails_with_high_Multimodality
(Mixture,
nu,
12 runs)
Pooled Chains results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
4.549 |
0.000782 |
11.953 |
| HMC |
3.0 |
5.179 |
0.00027 |
11.007 |
| HMC |
4.0 |
3.583 |
0.00424 |
15.656 |
| HMC |
10.0 |
6.962 |
2.31e-05 |
36.838 |
| HMC |
50.0 |
4.896 |
0.000468 |
30.587 |
| SMC |
2.1 |
3.450 |
0.0052 |
7.994 |
| SMC |
3.0 |
2.318 |
0.0346 |
1.621 |
| SMC |
4.0 |
2.082 |
0.0494 |
0.916 |
| SMC |
10.0 |
-0.909 |
0.375 |
-0.303 |
| SMC |
50.0 |
1.772 |
0.0923 |
0.928 |
| Metro |
2.1 |
3.611 |
0.00379 |
6.681 |
| Metro |
3.0 |
3.236 |
0.00769 |
8.367 |
| Metro |
4.0 |
4.069 |
0.00181 |
14.391 |
| Metro |
10.0 |
4.513 |
0.000874 |
29.963 |
| Metro |
50.0 |
5.723 |
0.000131 |
36.638 |
| DEMetro_Z |
2.1 |
2.739 |
0.0191 |
10.304 |
| DEMetro_Z |
3.0 |
5.476 |
0.000184 |
19.220 |
| DEMetro_Z |
4.0 |
4.883 |
0.000473 |
22.668 |
| DEMetro_Z |
10.0 |
3.702 |
0.00346 |
21.450 |
| DEMetro_Z |
50.0 |
3.565 |
0.00441 |
25.162 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
0.336
|
0.743
|
0.097
|
| HMC_vs_DEMetro_Z |
1
|
-2.320
|
0.0406
|
-0.670
|
| HMC_vs_DEMetro_Z |
2
|
-1.004
|
0.337
|
-0.290
|
| HMC_vs_DEMetro_Z |
3
|
2.561
|
0.0265
|
0.739
|
| HMC_vs_DEMetro_Z |
4
|
0.653
|
0.527
|
0.188
|
| Metro_vs_SMC |
0
|
-0.503
|
0.625
|
-0.145
|
| Metro_vs_SMC |
1
|
2.268
|
0.0445
|
0.655
|
| Metro_vs_SMC |
2
|
3.780
|
0.00305
|
1.091
|
| Metro_vs_SMC |
3
|
4.536
|
0.000849
|
1.309
|
| Metro_vs_SMC |
4
|
5.616
|
0.000157
|
1.621
|
| Metro_vs_DEMetro_Z |
0
|
-0.778
|
0.453
|
-0.224
|
| Metro_vs_DEMetro_Z |
1
|
-2.341
|
0.0391
|
-0.676
|
| Metro_vs_DEMetro_Z |
2
|
-1.618
|
0.134
|
-0.467
|
| Metro_vs_DEMetro_Z |
3
|
1.287
|
0.225
|
0.372
|
| Metro_vs_DEMetro_Z |
4
|
1.597
|
0.138
|
0.461
|
| HMC_vs_Metro |
0
|
1.770
|
0.104
|
0.511
|
| HMC_vs_Metro |
1
|
0.810
|
0.435
|
0.234
|
| HMC_vs_Metro |
2
|
0.246
|
0.81
|
0.071
|
| HMC_vs_Metro |
3
|
1.187
|
0.26
|
0.343
|
| HMC_vs_Metro |
4
|
-0.816
|
0.432
|
-0.236
|
| HMC_vs_SMC |
0
|
0.971
|
0.352
|
0.280
|
| HMC_vs_SMC |
1
|
4.036
|
0.00196
|
1.165
|
| HMC_vs_SMC |
2
|
3.297
|
0.00712
|
0.952
|
| HMC_vs_SMC |
3
|
7.084
|
2.03e-05
|
2.045
|
| HMC_vs_SMC |
4
|
4.898
|
0.000473
|
1.414
|
| DEMetro_Z_vs_SMC |
0
|
0.511
|
0.619
|
0.147
|
| DEMetro_Z_vs_SMC |
1
|
5.114
|
0.000337
|
1.476
|
| DEMetro_Z_vs_SMC |
2
|
4.874
|
0.000491
|
1.407
|
| DEMetro_Z_vs_SMC |
3
|
3.736
|
0.00329
|
1.079
|
| DEMetro_Z_vs_SMC |
4
|
3.547
|
0.00458
|
1.024
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.830 |
0.066 |
0.064 |
11.953 |
| HMC |
3.0 |
1.019 |
0.091 |
0.084 |
11.007 |
| HMC |
4.0 |
1.489 |
0.079 |
0.090 |
15.656 |
| HMC |
10.0 |
3.013 |
0.091 |
0.079 |
36.838 |
| HMC |
50.0 |
2.437 |
0.096 |
0.077 |
30.587 |
| SMC |
2.1 |
0.577 |
0.066 |
0.064 |
7.994 |
| SMC |
3.0 |
0.227 |
0.091 |
0.084 |
1.621 |
| SMC |
4.0 |
0.162 |
0.079 |
0.090 |
0.916 |
| SMC |
10.0 |
0.067 |
0.091 |
0.079 |
-0.303 |
| SMC |
50.0 |
0.167 |
0.096 |
0.077 |
0.928 |
| Metro |
2.1 |
0.493 |
0.066 |
0.064 |
6.681 |
| Metro |
3.0 |
0.796 |
0.091 |
0.084 |
8.367 |
| Metro |
4.0 |
1.375 |
0.079 |
0.090 |
14.391 |
| Metro |
10.0 |
2.467 |
0.091 |
0.079 |
29.963 |
| Metro |
50.0 |
2.900 |
0.096 |
0.077 |
36.638 |
| DEMetro_Z |
2.1 |
0.724 |
0.066 |
0.064 |
10.304 |
| DEMetro_Z |
3.0 |
1.712 |
0.091 |
0.084 |
19.220 |
| DEMetro_Z |
4.0 |
2.120 |
0.079 |
0.090 |
22.668 |
| DEMetro_Z |
10.0 |
1.792 |
0.091 |
0.079 |
21.450 |
| DEMetro_Z |
50.0 |
2.022 |
0.096 |
0.077 |
25.162 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
-1.448 |
0.175 |
-0.420 |
| HMC |
3.0 |
1.431 |
0.177 |
1.622 |
| HMC |
4.0 |
1.881 |
0.0867 |
40.404 |
| HMC |
10.0 |
3.864 |
0.00263 |
66.613 |
| HMC |
50.0 |
3.258 |
0.00762 |
69.392 |
| SMC |
2.1 |
-1.456 |
0.173 |
-0.422 |
| SMC |
3.0 |
-0.160 |
0.875 |
-0.049 |
| SMC |
4.0 |
0.903 |
0.379 |
0.520 |
| SMC |
10.0 |
-0.300 |
0.767 |
-0.106 |
| SMC |
50.0 |
-0.653 |
0.52 |
-0.265 |
| Metro |
2.1 |
-1.541 |
0.151 |
-0.446 |
| Metro |
3.0 |
1.465 |
0.169 |
2.135 |
| Metro |
4.0 |
2.889 |
0.0147 |
31.152 |
| Metro |
10.0 |
2.887 |
0.0148 |
55.230 |
| Metro |
50.0 |
3.505 |
0.00492 |
92.946 |
| DEMetro_Z |
2.1 |
-1.454 |
0.174 |
-0.421 |
| DEMetro_Z |
3.0 |
2.570 |
0.0258 |
8.693 |
| DEMetro_Z |
4.0 |
2.364 |
0.0375 |
65.619 |
| DEMetro_Z |
10.0 |
2.682 |
0.0213 |
33.263 |
| DEMetro_Z |
50.0 |
2.398 |
0.0354 |
59.844 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
0.048
|
0.962
|
0.014
|
| HMC_vs_SMC |
1
|
1.476
|
0.168
|
0.426
|
| HMC_vs_SMC |
2
|
1.876
|
0.0874
|
0.542
|
| HMC_vs_SMC |
3
|
3.862
|
0.00264
|
1.115
|
| HMC_vs_SMC |
4
|
3.284
|
0.00728
|
0.948
|
| Metro_vs_DEMetro_Z |
0
|
-1.129
|
0.283
|
-0.326
|
| Metro_vs_DEMetro_Z |
1
|
-1.682
|
0.121
|
-0.486
|
| Metro_vs_DEMetro_Z |
2
|
-1.135
|
0.281
|
-0.328
|
| Metro_vs_DEMetro_Z |
3
|
1.279
|
0.227
|
0.369
|
| Metro_vs_DEMetro_Z |
4
|
1.130
|
0.282
|
0.326
|
| HMC_vs_Metro |
0
|
0.796
|
0.443
|
0.230
|
| HMC_vs_Metro |
1
|
-0.266
|
0.795
|
-0.077
|
| HMC_vs_Metro |
2
|
0.376
|
0.714
|
0.108
|
| HMC_vs_Metro |
3
|
0.615
|
0.551
|
0.178
|
| HMC_vs_Metro |
4
|
-0.940
|
0.367
|
-0.271
|
| HMC_vs_DEMetro_Z |
0
|
0.022
|
0.983
|
0.006
|
| HMC_vs_DEMetro_Z |
1
|
-2.049
|
0.0651
|
-0.592
|
| HMC_vs_DEMetro_Z |
2
|
-0.648
|
0.53
|
-0.187
|
| HMC_vs_DEMetro_Z |
3
|
2.360
|
0.0378
|
0.681
|
| HMC_vs_DEMetro_Z |
4
|
0.301
|
0.769
|
0.087
|
| Metro_vs_SMC |
0
|
-0.782
|
0.451
|
-0.226
|
| Metro_vs_SMC |
1
|
1.538
|
0.152
|
0.444
|
| Metro_vs_SMC |
2
|
2.852
|
0.0157
|
0.823
|
| Metro_vs_SMC |
3
|
2.900
|
0.0144
|
0.837
|
| Metro_vs_SMC |
4
|
3.517
|
0.00483
|
1.015
|
| DEMetro_Z_vs_SMC |
0
|
0.028
|
0.979
|
0.008
|
| DEMetro_Z_vs_SMC |
1
|
2.558
|
0.0266
|
0.739
|
| DEMetro_Z_vs_SMC |
2
|
2.342
|
0.039
|
0.676
|
| DEMetro_Z_vs_SMC |
3
|
2.694
|
0.0209
|
0.778
|
| DEMetro_Z_vs_SMC |
4
|
2.398
|
0.0353
|
0.692
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
5.258 |
26.699 |
51.062 |
-0.420 |
| HMC |
3.0 |
1.752 |
0.764 |
0.609 |
1.622 |
| HMC |
4.0 |
5.544 |
0.284 |
0.130 |
40.404 |
| HMC |
10.0 |
16.071 |
0.283 |
0.237 |
66.613 |
| HMC |
50.0 |
11.326 |
0.268 |
0.159 |
69.392 |
| SMC |
2.1 |
5.167 |
26.699 |
51.062 |
-0.422 |
| SMC |
3.0 |
0.734 |
0.764 |
0.609 |
-0.049 |
| SMC |
4.0 |
0.352 |
0.284 |
0.130 |
0.520 |
| SMC |
10.0 |
0.258 |
0.283 |
0.237 |
-0.106 |
| SMC |
50.0 |
0.226 |
0.268 |
0.159 |
-0.265 |
| Metro |
2.1 |
3.938 |
26.699 |
51.062 |
-0.446 |
| Metro |
3.0 |
2.064 |
0.764 |
0.609 |
2.135 |
| Metro |
4.0 |
4.340 |
0.284 |
0.130 |
31.152 |
| Metro |
10.0 |
13.374 |
0.283 |
0.237 |
55.230 |
| Metro |
50.0 |
15.080 |
0.268 |
0.159 |
92.946 |
| DEMetro_Z |
2.1 |
5.219 |
26.699 |
51.062 |
-0.421 |
| DEMetro_Z |
3.0 |
6.059 |
0.764 |
0.609 |
8.693 |
| DEMetro_Z |
4.0 |
8.827 |
0.284 |
0.130 |
65.619 |
| DEMetro_Z |
10.0 |
8.167 |
0.283 |
0.237 |
33.263 |
| DEMetro_Z |
50.0 |
9.805 |
0.268 |
0.159 |
59.844 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
3.983 |
0.00192 |
6.783 |
| HMC |
3.0 |
5.153 |
0.000283 |
11.193 |
| HMC |
4.0 |
3.580 |
0.00428 |
17.675 |
| HMC |
10.0 |
6.561 |
3.97e-05 |
36.506 |
| HMC |
50.0 |
5.032 |
0.000378 |
33.687 |
| SMC |
2.1 |
5.856 |
5.9e-05 |
6.053 |
| SMC |
3.0 |
3.189 |
0.00583 |
2.157 |
| SMC |
4.0 |
2.251 |
0.035 |
1.002 |
| SMC |
10.0 |
-1.087 |
0.292 |
-0.355 |
| SMC |
50.0 |
1.902 |
0.0726 |
1.013 |
| Metro |
2.1 |
4.006 |
0.00149 |
3.970 |
| Metro |
3.0 |
3.417 |
0.00556 |
8.795 |
| Metro |
4.0 |
4.262 |
0.0013 |
16.094 |
| Metro |
10.0 |
4.474 |
0.000931 |
29.512 |
| Metro |
50.0 |
5.520 |
0.000179 |
39.642 |
| DEMetro_Z |
2.1 |
2.909 |
0.0138 |
6.548 |
| DEMetro_Z |
3.0 |
5.169 |
0.000299 |
20.651 |
| DEMetro_Z |
4.0 |
4.749 |
0.000592 |
25.500 |
| DEMetro_Z |
10.0 |
3.577 |
0.00431 |
21.774 |
| DEMetro_Z |
50.0 |
3.499 |
0.00496 |
27.497 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
-0.932
|
0.371
|
-0.269
|
| Metro_vs_DEMetro_Z |
1
|
-2.362
|
0.0377
|
-0.682
|
| Metro_vs_DEMetro_Z |
2
|
-1.741
|
0.109
|
-0.503
|
| Metro_vs_DEMetro_Z |
3
|
1.175
|
0.265
|
0.339
|
| Metro_vs_DEMetro_Z |
4
|
1.408
|
0.187
|
0.407
|
| DEMetro_Z_vs_SMC |
0
|
0.188
|
0.854
|
0.054
|
| DEMetro_Z_vs_SMC |
1
|
4.764
|
0.000586
|
1.375
|
| DEMetro_Z_vs_SMC |
2
|
4.740
|
0.000609
|
1.368
|
| DEMetro_Z_vs_SMC |
3
|
3.622
|
0.00401
|
1.046
|
| DEMetro_Z_vs_SMC |
4
|
3.478
|
0.00517
|
1.004
|
| HMC_vs_DEMetro_Z |
0
|
0.078
|
0.94
|
0.022
|
| HMC_vs_DEMetro_Z |
1
|
-2.339
|
0.0393
|
-0.675
|
| HMC_vs_DEMetro_Z |
2
|
-0.989
|
0.344
|
-0.286
|
| HMC_vs_DEMetro_Z |
3
|
2.348
|
0.0386
|
0.678
|
| HMC_vs_DEMetro_Z |
4
|
0.684
|
0.508
|
0.198
|
| HMC_vs_Metro |
0
|
1.536
|
0.153
|
0.444
|
| HMC_vs_Metro |
1
|
0.740
|
0.475
|
0.214
|
| HMC_vs_Metro |
2
|
0.281
|
0.784
|
0.081
|
| HMC_vs_Metro |
3
|
1.152
|
0.274
|
0.333
|
| HMC_vs_Metro |
4
|
-0.732
|
0.479
|
-0.211
|
| HMC_vs_SMC |
0
|
0.351
|
0.732
|
0.101
|
| HMC_vs_SMC |
1
|
3.821
|
0.00284
|
1.103
|
| HMC_vs_SMC |
2
|
3.310
|
0.00695
|
0.956
|
| HMC_vs_SMC |
3
|
6.683
|
3.45e-05
|
1.929
|
| HMC_vs_SMC |
4
|
5.056
|
0.000369
|
1.460
|
| Metro_vs_SMC |
0
|
-1.660
|
0.125
|
-0.479
|
| Metro_vs_SMC |
1
|
2.272
|
0.0442
|
0.656
|
| Metro_vs_SMC |
2
|
3.997
|
0.0021
|
1.154
|
| Metro_vs_SMC |
3
|
4.519
|
0.000874
|
1.304
|
| Metro_vs_SMC |
4
|
5.421
|
0.00021
|
1.565
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.843 |
0.182 |
0.098 |
6.783 |
| HMC |
3.0 |
0.913 |
0.130 |
0.070 |
11.193 |
| HMC |
4.0 |
1.360 |
0.108 |
0.071 |
17.675 |
| HMC |
10.0 |
2.719 |
0.110 |
0.071 |
36.506 |
| HMC |
50.0 |
2.192 |
0.106 |
0.062 |
33.687 |
| SMC |
2.1 |
0.772 |
0.182 |
0.098 |
6.053 |
| SMC |
3.0 |
0.281 |
0.130 |
0.070 |
2.157 |
| SMC |
4.0 |
0.179 |
0.108 |
0.071 |
1.002 |
| SMC |
10.0 |
0.085 |
0.110 |
0.071 |
-0.355 |
| SMC |
50.0 |
0.169 |
0.106 |
0.062 |
1.013 |
| Metro |
2.1 |
0.569 |
0.182 |
0.098 |
3.970 |
| Metro |
3.0 |
0.745 |
0.130 |
0.070 |
8.795 |
| Metro |
4.0 |
1.248 |
0.108 |
0.071 |
16.094 |
| Metro |
10.0 |
2.220 |
0.110 |
0.071 |
29.512 |
| Metro |
50.0 |
2.561 |
0.106 |
0.062 |
39.642 |
| DEMetro_Z |
2.1 |
0.821 |
0.182 |
0.098 |
6.548 |
| DEMetro_Z |
3.0 |
1.574 |
0.130 |
0.070 |
20.651 |
| DEMetro_Z |
4.0 |
1.914 |
0.108 |
0.071 |
25.500 |
| DEMetro_Z |
10.0 |
1.667 |
0.110 |
0.071 |
21.774 |
| DEMetro_Z |
50.0 |
1.809 |
0.106 |
0.062 |
27.497 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
4.191 |
0.00145 |
12.652 |
| HMC |
3.0 |
4.651 |
0.000664 |
12.791 |
| HMC |
4.0 |
3.564 |
0.00439 |
17.553 |
| HMC |
10.0 |
7.449 |
1.24e-05 |
39.741 |
| HMC |
50.0 |
5.105 |
0.000337 |
34.538 |
| SMC |
2.1 |
3.933 |
0.0022 |
8.983 |
| SMC |
3.0 |
2.724 |
0.015 |
1.796 |
| SMC |
4.0 |
2.078 |
0.0498 |
0.918 |
| SMC |
10.0 |
-0.790 |
0.44 |
-0.268 |
| SMC |
50.0 |
1.903 |
0.0725 |
1.013 |
| Metro |
2.1 |
3.799 |
0.00273 |
7.342 |
| Metro |
3.0 |
2.942 |
0.0132 |
9.748 |
| Metro |
4.0 |
4.090 |
0.00175 |
16.349 |
| Metro |
10.0 |
4.661 |
0.000686 |
32.534 |
| Metro |
50.0 |
5.896 |
0.000102 |
41.491 |
| DEMetro_Z |
2.1 |
2.694 |
0.0207 |
11.748 |
| DEMetro_Z |
3.0 |
5.077 |
0.000349 |
23.989 |
| DEMetro_Z |
4.0 |
5.064 |
0.000357 |
25.789 |
| DEMetro_Z |
10.0 |
3.709 |
0.00342 |
23.729 |
| DEMetro_Z |
50.0 |
3.754 |
0.00317 |
28.413 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
0.542
|
0.599
|
0.156
|
| DEMetro_Z_vs_SMC |
1
|
4.681
|
0.000671
|
1.351
|
| DEMetro_Z_vs_SMC |
2
|
5.044
|
0.000376
|
1.456
|
| DEMetro_Z_vs_SMC |
3
|
3.730
|
0.00332
|
1.077
|
| DEMetro_Z_vs_SMC |
4
|
3.749
|
0.00322
|
1.082
|
| HMC_vs_Metro |
0
|
1.599
|
0.138
|
0.462
|
| HMC_vs_Metro |
1
|
0.738
|
0.476
|
0.213
|
| HMC_vs_Metro |
2
|
0.206
|
0.841
|
0.059
|
| HMC_vs_Metro |
3
|
1.182
|
0.262
|
0.341
|
| HMC_vs_Metro |
4
|
-0.834
|
0.422
|
-0.241
|
| Metro_vs_DEMetro_Z |
0
|
-0.825
|
0.427
|
-0.238
|
| Metro_vs_DEMetro_Z |
1
|
-2.374
|
0.0369
|
-0.685
|
| Metro_vs_DEMetro_Z |
2
|
-1.700
|
0.117
|
-0.491
|
| Metro_vs_DEMetro_Z |
3
|
1.205
|
0.254
|
0.348
|
| Metro_vs_DEMetro_Z |
4
|
1.704
|
0.117
|
0.492
|
| HMC_vs_SMC |
0
|
0.827
|
0.426
|
0.239
|
| HMC_vs_SMC |
1
|
3.701
|
0.0035
|
1.068
|
| HMC_vs_SMC |
2
|
3.317
|
0.00687
|
0.958
|
| HMC_vs_SMC |
3
|
7.565
|
1.11e-05
|
2.184
|
| HMC_vs_SMC |
4
|
5.135
|
0.000326
|
1.482
|
| Metro_vs_SMC |
0
|
-0.610
|
0.554
|
-0.176
|
| Metro_vs_SMC |
1
|
2.158
|
0.0539
|
0.623
|
| Metro_vs_SMC |
2
|
3.837
|
0.00276
|
1.108
|
| Metro_vs_SMC |
3
|
4.671
|
0.000682
|
1.348
|
| Metro_vs_SMC |
4
|
5.832
|
0.000114
|
1.683
|
| HMC_vs_DEMetro_Z |
0
|
0.162
|
0.874
|
0.047
|
| HMC_vs_DEMetro_Z |
1
|
-2.383
|
0.0363
|
-0.688
|
| HMC_vs_DEMetro_Z |
2
|
-1.073
|
0.306
|
-0.310
|
| HMC_vs_DEMetro_Z |
3
|
2.408
|
0.0347
|
0.695
|
| HMC_vs_DEMetro_Z |
4
|
0.686
|
0.507
|
0.198
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.082 |
0.009 |
0.006 |
12.652 |
| HMC |
3.0 |
0.110 |
0.010 |
0.008 |
12.791 |
| HMC |
4.0 |
0.167 |
0.009 |
0.009 |
17.553 |
| HMC |
10.0 |
0.339 |
0.010 |
0.008 |
39.741 |
| HMC |
50.0 |
0.278 |
0.010 |
0.008 |
34.538 |
| SMC |
2.1 |
0.061 |
0.009 |
0.006 |
8.983 |
| SMC |
3.0 |
0.024 |
0.010 |
0.008 |
1.796 |
| SMC |
4.0 |
0.017 |
0.009 |
0.009 |
0.918 |
| SMC |
10.0 |
0.008 |
0.010 |
0.008 |
-0.268 |
| SMC |
50.0 |
0.018 |
0.010 |
0.008 |
1.013 |
| Metro |
2.1 |
0.051 |
0.009 |
0.006 |
7.342 |
| Metro |
3.0 |
0.086 |
0.010 |
0.008 |
9.748 |
| Metro |
4.0 |
0.156 |
0.009 |
0.009 |
16.349 |
| Metro |
10.0 |
0.279 |
0.010 |
0.008 |
32.534 |
| Metro |
50.0 |
0.332 |
0.010 |
0.008 |
41.491 |
| DEMetro_Z |
2.1 |
0.077 |
0.009 |
0.006 |
11.748 |
| DEMetro_Z |
3.0 |
0.197 |
0.010 |
0.008 |
23.989 |
| DEMetro_Z |
4.0 |
0.241 |
0.009 |
0.009 |
25.789 |
| DEMetro_Z |
10.0 |
0.207 |
0.010 |
0.008 |
23.729 |
| DEMetro_Z |
50.0 |
0.230 |
0.010 |
0.008 |
28.413 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
R Hat (scatter)
Mode Transitions
One Chain results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
4.142 |
0.00156 |
11.270 |
| HMC |
3.0 |
6.560 |
3.5e-05 |
14.852 |
| HMC |
4.0 |
5.270 |
0.00026 |
28.756 |
| HMC |
10.0 |
24.746 |
3.61e-11 |
66.559 |
| HMC |
50.0 |
131.836 |
6.54e-29 |
71.808 |
| SMC |
2.1 |
3.292 |
0.00705 |
10.959 |
| SMC |
3.0 |
1.062 |
0.301 |
0.507 |
| SMC |
4.0 |
-0.232 |
0.82 |
-0.074 |
| SMC |
10.0 |
0.834 |
0.413 |
0.320 |
| SMC |
50.0 |
0.868 |
0.395 |
0.352 |
| Metro |
2.1 |
4.434 |
0.000699 |
4.636 |
| Metro |
3.0 |
1.780 |
0.102 |
8.708 |
| Metro |
4.0 |
2.310 |
0.0412 |
11.986 |
| Metro |
10.0 |
20.144 |
3.91e-10 |
66.162 |
| Metro |
50.0 |
140.408 |
9.21e-31 |
71.590 |
| DEMetro_Z |
2.1 |
2.995 |
0.0122 |
24.150 |
| DEMetro_Z |
3.0 |
2.953 |
0.0131 |
18.755 |
| DEMetro_Z |
4.0 |
2.914 |
0.014 |
21.786 |
| DEMetro_Z |
10.0 |
3.098 |
0.0101 |
31.137 |
| DEMetro_Z |
50.0 |
7.786 |
8.31e-06 |
61.054 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
-1.415
|
0.185
|
-0.409
|
| HMC_vs_DEMetro_Z |
1
|
-0.571
|
0.579
|
-0.165
|
| HMC_vs_DEMetro_Z |
2
|
0.627
|
0.543
|
0.181
|
| HMC_vs_DEMetro_Z |
3
|
3.716
|
0.00341
|
1.073
|
| HMC_vs_DEMetro_Z |
4
|
1.355
|
0.203
|
0.391
|
| Metro_vs_SMC |
0
|
-1.739
|
0.11
|
-0.502
|
| Metro_vs_SMC |
1
|
1.664
|
0.124
|
0.480
|
| Metro_vs_SMC |
2
|
2.346
|
0.0387
|
0.677
|
| Metro_vs_SMC |
3
|
19.218
|
8.19e-10
|
5.548
|
| Metro_vs_SMC |
4
|
126.155
|
9.72e-19
|
36.418
|
| Metro_vs_DEMetro_Z |
0
|
-2.385
|
0.0362
|
-0.689
|
| Metro_vs_DEMetro_Z |
1
|
-1.092
|
0.298
|
-0.315
|
| Metro_vs_DEMetro_Z |
2
|
-0.955
|
0.36
|
-0.276
|
| Metro_vs_DEMetro_Z |
3
|
3.037
|
0.0113
|
0.877
|
| Metro_vs_DEMetro_Z |
4
|
1.364
|
0.2
|
0.394
|
| HMC_vs_Metro |
0
|
2.808
|
0.017
|
0.810
|
| HMC_vs_Metro |
1
|
0.957
|
0.359
|
0.276
|
| HMC_vs_Metro |
2
|
3.446
|
0.00546
|
0.995
|
| HMC_vs_Metro |
3
|
0.091
|
0.929
|
0.026
|
| HMC_vs_Metro |
4
|
0.811
|
0.435
|
0.234
|
| HMC_vs_SMC |
0
|
0.089
|
0.93
|
0.026
|
| HMC_vs_SMC |
1
|
6.366
|
5.33e-05
|
1.838
|
| HMC_vs_SMC |
2
|
5.322
|
0.000244
|
1.536
|
| HMC_vs_SMC |
3
|
25.625
|
3.69e-11
|
7.397
|
| HMC_vs_SMC |
4
|
118.205
|
1.99e-18
|
34.123
|
| DEMetro_Z_vs_SMC |
0
|
1.752
|
0.108
|
0.506
|
| DEMetro_Z_vs_SMC |
1
|
2.846
|
0.0159
|
0.822
|
| DEMetro_Z_vs_SMC |
2
|
2.921
|
0.0139
|
0.843
|
| DEMetro_Z_vs_SMC |
3
|
3.083
|
0.0104
|
0.890
|
| DEMetro_Z_vs_SMC |
4
|
7.750
|
8.82e-06
|
2.237
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.786 |
0.066 |
0.064 |
11.270 |
| HMC |
3.0 |
1.343 |
0.091 |
0.084 |
14.852 |
| HMC |
4.0 |
2.668 |
0.079 |
0.090 |
28.756 |
| HMC |
10.0 |
5.370 |
0.091 |
0.079 |
66.559 |
| HMC |
50.0 |
5.591 |
0.096 |
0.077 |
71.808 |
| SMC |
2.1 |
0.766 |
0.066 |
0.064 |
10.959 |
| SMC |
3.0 |
0.134 |
0.091 |
0.084 |
0.507 |
| SMC |
4.0 |
0.072 |
0.079 |
0.090 |
-0.074 |
| SMC |
10.0 |
0.117 |
0.091 |
0.079 |
0.320 |
| SMC |
50.0 |
0.123 |
0.096 |
0.077 |
0.352 |
| Metro |
2.1 |
0.362 |
0.066 |
0.064 |
4.636 |
| Metro |
3.0 |
0.825 |
0.091 |
0.084 |
8.708 |
| Metro |
4.0 |
1.158 |
0.079 |
0.090 |
11.986 |
| Metro |
10.0 |
5.338 |
0.091 |
0.079 |
66.162 |
| Metro |
50.0 |
5.574 |
0.096 |
0.077 |
71.590 |
| DEMetro_Z |
2.1 |
1.609 |
0.066 |
0.064 |
24.150 |
| DEMetro_Z |
3.0 |
1.672 |
0.091 |
0.084 |
18.755 |
| DEMetro_Z |
4.0 |
2.040 |
0.079 |
0.090 |
21.786 |
| DEMetro_Z |
10.0 |
2.561 |
0.091 |
0.079 |
31.137 |
| DEMetro_Z |
50.0 |
4.768 |
0.096 |
0.077 |
61.054 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
0.283 |
0.781 |
0.208 |
| HMC |
3.0 |
3.685 |
0.00284 |
3.946 |
| HMC |
4.0 |
3.681 |
0.00362 |
105.283 |
| HMC |
10.0 |
15.035 |
1.1e-08 |
174.452 |
| HMC |
50.0 |
703.170 |
2.57e-49 |
282.170 |
| SMC |
2.1 |
-1.527 |
0.155 |
-0.442 |
| SMC |
3.0 |
-0.872 |
0.395 |
-0.286 |
| SMC |
4.0 |
1.335 |
0.203 |
1.075 |
| SMC |
10.0 |
-1.635 |
0.121 |
-0.532 |
| SMC |
50.0 |
-0.592 |
0.56 |
-0.266 |
| Metro |
2.1 |
-1.594 |
0.139 |
-0.461 |
| Metro |
3.0 |
1.250 |
0.237 |
5.791 |
| Metro |
4.0 |
1.413 |
0.185 |
41.127 |
| Metro |
10.0 |
14.009 |
2.31e-08 |
177.434 |
| Metro |
50.0 |
701.162 |
2.64e-49 |
282.152 |
| DEMetro_Z |
2.1 |
-1.008 |
0.332 |
-0.303 |
| DEMetro_Z |
3.0 |
1.940 |
0.0783 |
13.386 |
| DEMetro_Z |
4.0 |
2.264 |
0.0448 |
100.671 |
| DEMetro_Z |
10.0 |
2.853 |
0.0157 |
79.870 |
| DEMetro_Z |
50.0 |
7.389 |
1.38e-05 |
234.923 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
0.967
|
0.354
|
0.279
|
| HMC_vs_SMC |
1
|
3.901
|
0.00247
|
1.126
|
| HMC_vs_SMC |
2
|
3.631
|
0.00395
|
1.048
|
| HMC_vs_SMC |
3
|
15.149
|
1.03e-08
|
4.373
|
| HMC_vs_SMC |
4
|
619.001
|
2.46e-26
|
178.690
|
| Metro_vs_DEMetro_Z |
0
|
-1.914
|
0.082
|
-0.553
|
| Metro_vs_DEMetro_Z |
1
|
-0.844
|
0.417
|
-0.244
|
| Metro_vs_DEMetro_Z |
2
|
-1.023
|
0.328
|
-0.295
|
| Metro_vs_DEMetro_Z |
3
|
2.820
|
0.0167
|
0.814
|
| Metro_vs_DEMetro_Z |
4
|
1.491
|
0.164
|
0.430
|
| HMC_vs_Metro |
0
|
0.986
|
0.345
|
0.285
|
| HMC_vs_Metro |
1
|
-0.360
|
0.725
|
-0.104
|
| HMC_vs_Metro |
2
|
2.417
|
0.0342
|
0.698
|
| HMC_vs_Metro |
3
|
-0.165
|
0.872
|
-0.048
|
| HMC_vs_Metro |
4
|
0.236
|
0.818
|
0.068
|
| HMC_vs_DEMetro_Z |
0
|
0.737
|
0.477
|
0.213
|
| HMC_vs_DEMetro_Z |
1
|
-1.347
|
0.205
|
-0.389
|
| HMC_vs_DEMetro_Z |
2
|
0.077
|
0.94
|
0.022
|
| HMC_vs_DEMetro_Z |
3
|
3.590
|
0.00425
|
1.036
|
| HMC_vs_DEMetro_Z |
4
|
1.490
|
0.164
|
0.430
|
| Metro_vs_SMC |
0
|
-1.027
|
0.326
|
-0.297
|
| Metro_vs_SMC |
1
|
1.292
|
0.223
|
0.373
|
| Metro_vs_SMC |
2
|
1.363
|
0.2
|
0.394
|
| Metro_vs_SMC |
3
|
14.095
|
2.19e-08
|
4.069
|
| Metro_vs_SMC |
4
|
594.398
|
3.84e-26
|
171.588
|
| DEMetro_Z_vs_SMC |
0
|
1.824
|
0.0954
|
0.527
|
| DEMetro_Z_vs_SMC |
1
|
1.974
|
0.0741
|
0.570
|
| DEMetro_Z_vs_SMC |
2
|
2.246
|
0.0462
|
0.648
|
| DEMetro_Z_vs_SMC |
3
|
2.870
|
0.0152
|
0.829
|
| DEMetro_Z_vs_SMC |
4
|
7.380
|
1.39e-05
|
2.130
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
37.344 |
26.699 |
51.062 |
0.208 |
| HMC |
3.0 |
3.167 |
0.764 |
0.609 |
3.946 |
| HMC |
4.0 |
13.990 |
0.284 |
0.130 |
105.283 |
| HMC |
10.0 |
41.630 |
0.283 |
0.237 |
174.452 |
| HMC |
50.0 |
45.233 |
0.268 |
0.159 |
282.170 |
| SMC |
2.1 |
4.139 |
26.699 |
51.062 |
-0.442 |
| SMC |
3.0 |
0.590 |
0.764 |
0.609 |
-0.286 |
| SMC |
4.0 |
0.424 |
0.284 |
0.130 |
1.075 |
| SMC |
10.0 |
0.157 |
0.283 |
0.237 |
-0.532 |
| SMC |
50.0 |
0.226 |
0.268 |
0.159 |
-0.266 |
| Metro |
2.1 |
3.181 |
26.699 |
51.062 |
-0.461 |
| Metro |
3.0 |
4.291 |
0.764 |
0.609 |
5.791 |
| Metro |
4.0 |
5.638 |
0.284 |
0.130 |
41.127 |
| Metro |
10.0 |
42.337 |
0.283 |
0.237 |
177.434 |
| Metro |
50.0 |
45.230 |
0.268 |
0.159 |
282.152 |
| DEMetro_Z |
2.1 |
11.230 |
26.699 |
51.062 |
-0.303 |
| DEMetro_Z |
3.0 |
8.917 |
0.764 |
0.609 |
13.386 |
| DEMetro_Z |
4.0 |
13.390 |
0.284 |
0.130 |
100.671 |
| DEMetro_Z |
10.0 |
19.213 |
0.283 |
0.237 |
79.870 |
| DEMetro_Z |
50.0 |
37.704 |
0.268 |
0.159 |
234.923 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
2.926 |
0.0134 |
6.779 |
| HMC |
3.0 |
6.446 |
4.21e-05 |
15.988 |
| HMC |
4.0 |
5.227 |
0.000278 |
32.952 |
| HMC |
10.0 |
21.962 |
1.43e-10 |
64.631 |
| HMC |
50.0 |
45.810 |
1.77e-14 |
80.690 |
| SMC |
2.1 |
3.372 |
0.00587 |
6.513 |
| SMC |
3.0 |
1.234 |
0.231 |
0.565 |
| SMC |
4.0 |
-0.177 |
0.862 |
-0.055 |
| SMC |
10.0 |
0.508 |
0.617 |
0.190 |
| SMC |
50.0 |
0.677 |
0.506 |
0.288 |
| Metro |
2.1 |
4.062 |
0.000879 |
2.602 |
| Metro |
3.0 |
1.766 |
0.105 |
10.028 |
| Metro |
4.0 |
2.186 |
0.0512 |
14.255 |
| Metro |
10.0 |
20.228 |
3.74e-10 |
66.422 |
| Metro |
50.0 |
43.527 |
3.34e-14 |
78.004 |
| DEMetro_Z |
2.1 |
3.188 |
0.00853 |
13.297 |
| DEMetro_Z |
3.0 |
3.155 |
0.00911 |
19.724 |
| DEMetro_Z |
4.0 |
2.940 |
0.0134 |
25.831 |
| DEMetro_Z |
10.0 |
3.085 |
0.0104 |
30.633 |
| DEMetro_Z |
50.0 |
7.728 |
8.93e-06 |
64.883 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
-2.540
|
0.0275
|
-0.733
|
| Metro_vs_DEMetro_Z |
1
|
-1.004
|
0.337
|
-0.290
|
| Metro_vs_DEMetro_Z |
2
|
-0.940
|
0.368
|
-0.271
|
| Metro_vs_DEMetro_Z |
3
|
3.087
|
0.0103
|
0.891
|
| Metro_vs_DEMetro_Z |
4
|
1.587
|
0.141
|
0.458
|
| DEMetro_Z_vs_SMC |
0
|
1.717
|
0.114
|
0.496
|
| DEMetro_Z_vs_SMC |
1
|
3.056
|
0.0109
|
0.882
|
| DEMetro_Z_vs_SMC |
2
|
2.948
|
0.0132
|
0.851
|
| DEMetro_Z_vs_SMC |
3
|
3.086
|
0.0104
|
0.891
|
| DEMetro_Z_vs_SMC |
4
|
7.714
|
9.22e-06
|
2.227
|
| HMC_vs_DEMetro_Z |
0
|
-1.296
|
0.221
|
-0.374
|
| HMC_vs_DEMetro_Z |
1
|
-0.549
|
0.594
|
-0.159
|
| HMC_vs_DEMetro_Z |
2
|
0.547
|
0.595
|
0.158
|
| HMC_vs_DEMetro_Z |
3
|
3.429
|
0.00564
|
0.990
|
| HMC_vs_DEMetro_Z |
4
|
1.709
|
0.116
|
0.493
|
| HMC_vs_Metro |
0
|
2.096
|
0.06
|
0.605
|
| HMC_vs_Metro |
1
|
0.814
|
0.433
|
0.235
|
| HMC_vs_Metro |
2
|
3.098
|
0.0101
|
0.894
|
| HMC_vs_Metro |
3
|
-0.391
|
0.703
|
-0.113
|
| HMC_vs_Metro |
4
|
0.987
|
0.345
|
0.285
|
| HMC_vs_SMC |
0
|
0.125
|
0.903
|
0.036
|
| HMC_vs_SMC |
1
|
6.262
|
6.16e-05
|
1.808
|
| HMC_vs_SMC |
2
|
5.265
|
0.000267
|
1.520
|
| HMC_vs_SMC |
3
|
22.724
|
1.35e-10
|
6.560
|
| HMC_vs_SMC |
4
|
43.133
|
1.27e-13
|
12.451
|
| Metro_vs_SMC |
0
|
-1.945
|
0.0778
|
-0.561
|
| Metro_vs_SMC |
1
|
1.657
|
0.126
|
0.478
|
| Metro_vs_SMC |
2
|
2.208
|
0.0494
|
0.638
|
| Metro_vs_SMC |
3
|
19.603
|
6.63e-10
|
5.659
|
| Metro_vs_SMC |
4
|
39.686
|
3.15e-13
|
11.456
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.843 |
0.182 |
0.098 |
6.779 |
| HMC |
3.0 |
1.248 |
0.130 |
0.070 |
15.988 |
| HMC |
4.0 |
2.441 |
0.108 |
0.071 |
32.952 |
| HMC |
10.0 |
4.730 |
0.110 |
0.071 |
64.631 |
| HMC |
50.0 |
5.104 |
0.106 |
0.062 |
80.690 |
| SMC |
2.1 |
0.817 |
0.182 |
0.098 |
6.513 |
| SMC |
3.0 |
0.170 |
0.130 |
0.070 |
0.565 |
| SMC |
4.0 |
0.104 |
0.108 |
0.071 |
-0.055 |
| SMC |
10.0 |
0.124 |
0.110 |
0.071 |
0.190 |
| SMC |
50.0 |
0.124 |
0.106 |
0.062 |
0.288 |
| Metro |
2.1 |
0.436 |
0.182 |
0.098 |
2.602 |
| Metro |
3.0 |
0.831 |
0.130 |
0.070 |
10.028 |
| Metro |
4.0 |
1.117 |
0.108 |
0.071 |
14.255 |
| Metro |
10.0 |
4.858 |
0.110 |
0.071 |
66.422 |
| Metro |
50.0 |
4.937 |
0.106 |
0.062 |
78.004 |
| DEMetro_Z |
2.1 |
1.479 |
0.182 |
0.098 |
13.297 |
| DEMetro_Z |
3.0 |
1.509 |
0.130 |
0.070 |
19.724 |
| DEMetro_Z |
4.0 |
1.937 |
0.108 |
0.071 |
25.831 |
| DEMetro_Z |
10.0 |
2.300 |
0.110 |
0.071 |
30.633 |
| DEMetro_Z |
50.0 |
4.125 |
0.106 |
0.062 |
64.883 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
4.067 |
0.00179 |
11.536 |
| HMC |
3.0 |
6.430 |
4.39e-05 |
17.397 |
| HMC |
4.0 |
5.384 |
0.000218 |
32.294 |
| HMC |
10.0 |
25.967 |
2.13e-11 |
70.606 |
| HMC |
50.0 |
108.942 |
2.69e-23 |
78.053 |
| SMC |
2.1 |
2.947 |
0.0132 |
12.681 |
| SMC |
3.0 |
1.331 |
0.198 |
0.655 |
| SMC |
4.0 |
-0.167 |
0.87 |
-0.052 |
| SMC |
10.0 |
0.979 |
0.338 |
0.387 |
| SMC |
50.0 |
0.863 |
0.397 |
0.347 |
| Metro |
2.1 |
3.921 |
0.00191 |
4.620 |
| Metro |
3.0 |
1.789 |
0.101 |
10.309 |
| Metro |
4.0 |
2.323 |
0.0403 |
13.230 |
| Metro |
10.0 |
21.055 |
2.43e-10 |
69.724 |
| Metro |
50.0 |
142.952 |
1.07e-29 |
77.329 |
| DEMetro_Z |
2.1 |
2.844 |
0.0159 |
28.680 |
| DEMetro_Z |
3.0 |
2.958 |
0.013 |
22.757 |
| DEMetro_Z |
4.0 |
2.927 |
0.0137 |
23.945 |
| DEMetro_Z |
10.0 |
3.129 |
0.00958 |
33.530 |
| DEMetro_Z |
50.0 |
7.751 |
8.69e-06 |
65.037 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
1.687
|
0.12
|
0.487
|
| DEMetro_Z_vs_SMC |
1
|
2.856
|
0.0156
|
0.824
|
| DEMetro_Z_vs_SMC |
2
|
2.931
|
0.0137
|
0.846
|
| DEMetro_Z_vs_SMC |
3
|
3.119
|
0.00977
|
0.900
|
| DEMetro_Z_vs_SMC |
4
|
7.726
|
9.09e-06
|
2.230
|
| HMC_vs_Metro |
0
|
3.023
|
0.0116
|
0.873
|
| HMC_vs_Metro |
1
|
0.935
|
0.37
|
0.270
|
| HMC_vs_Metro |
2
|
3.582
|
0.0043
|
1.034
|
| HMC_vs_Metro |
3
|
0.203
|
0.843
|
0.059
|
| HMC_vs_Metro |
4
|
0.995
|
0.341
|
0.287
|
| Metro_vs_DEMetro_Z |
0
|
-2.325
|
0.0402
|
-0.671
|
| Metro_vs_DEMetro_Z |
1
|
-1.135
|
0.28
|
-0.328
|
| Metro_vs_DEMetro_Z |
2
|
-0.953
|
0.361
|
-0.275
|
| Metro_vs_DEMetro_Z |
3
|
2.963
|
0.0129
|
0.855
|
| Metro_vs_DEMetro_Z |
4
|
1.500
|
0.162
|
0.433
|
| HMC_vs_SMC |
0
|
-0.271
|
0.792
|
-0.078
|
| HMC_vs_SMC |
1
|
6.235
|
6.39e-05
|
1.800
|
| HMC_vs_SMC |
2
|
5.425
|
0.000209
|
1.566
|
| HMC_vs_SMC |
3
|
26.721
|
2.34e-11
|
7.714
|
| HMC_vs_SMC |
4
|
97.318
|
1.68e-17
|
28.093
|
| Metro_vs_SMC |
0
|
-1.819
|
0.0962
|
-0.525
|
| Metro_vs_SMC |
1
|
1.663
|
0.124
|
0.480
|
| Metro_vs_SMC |
2
|
2.350
|
0.0385
|
0.678
|
| Metro_vs_SMC |
3
|
19.895
|
5.65e-10
|
5.743
|
| Metro_vs_SMC |
4
|
141.032
|
2.85e-19
|
40.712
|
| HMC_vs_DEMetro_Z |
0
|
-1.530
|
0.154
|
-0.442
|
| HMC_vs_DEMetro_Z |
1
|
-0.639
|
0.536
|
-0.184
|
| HMC_vs_DEMetro_Z |
2
|
0.686
|
0.507
|
0.198
|
| HMC_vs_DEMetro_Z |
3
|
3.633
|
0.00394
|
1.049
|
| HMC_vs_DEMetro_Z |
4
|
1.521
|
0.156
|
0.439
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.075 |
0.009 |
0.006 |
11.536 |
| HMC |
3.0 |
0.146 |
0.010 |
0.008 |
17.397 |
| HMC |
4.0 |
0.300 |
0.009 |
0.009 |
32.294 |
| HMC |
10.0 |
0.594 |
0.010 |
0.008 |
70.606 |
| HMC |
50.0 |
0.615 |
0.010 |
0.008 |
78.053 |
| SMC |
2.1 |
0.082 |
0.009 |
0.006 |
12.681 |
| SMC |
3.0 |
0.015 |
0.010 |
0.008 |
0.655 |
| SMC |
4.0 |
0.009 |
0.009 |
0.009 |
-0.052 |
| SMC |
10.0 |
0.014 |
0.010 |
0.008 |
0.387 |
| SMC |
50.0 |
0.013 |
0.010 |
0.008 |
0.347 |
| Metro |
2.1 |
0.035 |
0.009 |
0.006 |
4.620 |
| Metro |
3.0 |
0.090 |
0.010 |
0.008 |
10.309 |
| Metro |
4.0 |
0.128 |
0.009 |
0.009 |
13.230 |
| Metro |
10.0 |
0.587 |
0.010 |
0.008 |
69.724 |
| Metro |
50.0 |
0.609 |
0.010 |
0.008 |
77.329 |
| DEMetro_Z |
2.1 |
0.174 |
0.009 |
0.006 |
28.680 |
| DEMetro_Z |
3.0 |
0.188 |
0.010 |
0.008 |
22.757 |
| DEMetro_Z |
4.0 |
0.225 |
0.009 |
0.009 |
23.945 |
| DEMetro_Z |
10.0 |
0.288 |
0.010 |
0.008 |
33.530 |
| DEMetro_Z |
50.0 |
0.514 |
0.010 |
0.008 |
65.037 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
Mode Transitions
Mode Transitions (scatter)
KDE + Init Plots
Forest & Ridge Plots
Pooled
Chain
Pairwise Scatter Plots
Pooled
Chain